This study is part of a Phd thesis on fluid apparent motion estimation with application to oceanography and meteorology. We estimate sea surface streams using divergence free conservation equation coupled with a second order div-curl regularisation. The problem is solved in a vector splines framework and follows the work of Suter  : the vector spline is uniquely defined given a set of control points, defined by local image criteria such as the motion index.

However, the basis functions introduced in Suter's work grow arbitrary large whenever r, rbeing the distance to control points, with two consequences: first, evaluation of the solution at a single point depends on the whole set of control points, and second, computation of the coefficients of the solution involves inverting a dense and ill-conditionned matrix. These problems lead to prohibitive computational costs in case of large data sets.

A partition of unity is proposed to circumvent these problems. The idea is to first subdivise the image into smaller regions. The motion is then computed in each small region using vector splines: as the regions are small and contain a small number of control points, the vector spline estimation is numerically stable. Finally, all motion fields, defined in small regions, are merged into a single one defined on the whole domain.

The definition of smaller regions is based on an iterative quadtree subdivision approach: starting from an unique region (the image domain), each region is subdivided if it contains more than a fixed number of control points.

In order to minimize aliasing effects at the limits between regions, the vector splines are computed in balls centered on the quadtree cells, so that the vector splines of adjacent regions intersect. The overall solution is obtained by summing up every vector spline, computed in individual regions, weighted by local coefficients depending on the distance to the centre of the associated quadtree cell.

Figure  displays a result from the model on a synthetic oceanographic image sequence: left, a 193 cells quadtree is built from 6085 control points, defined according to local criteria (gradient norm and motion index) in the image. The subdvision is controlled in such a way that each cell contains no more than 200 points. The resulting motion field is displayed on the right side of figure  .

Oceanographic (current) and meteorological (winds) fluid flows are characterised by turbulence and hence the presence of structures of different temporal and spatial scales. The vector splines approach to motion estimation is adapted to oceanography (brightness conservation) and meteorology (mass transport equation) and preserves the rotatioanal patterns of the flow owing to its div-curl regularity constraint. But it needs to be formulated in a multiscale framework.

The multiscale approach is tackled by using compactly supported radial basis functions centered at Voronoï points of X. The set of Voronoï points V_Xdefines an irregular grid which is connected to the spatial distribution of the original control points set. We define various scales by applying a thinningalgorithm  to the set V_X. The thinning algorithm provides a decomposition of V_Xinto a nested sequence of subsets in such a way that the points in each subset are distributed as evenly as possible and their spatial density increases smoothly.

At each scale, we solve a least square problem to find coefficients of the solution. The system is large and consists in two terms: a term for the conservation equation and a regularization term which consists in a discretisation of partial differential operators applied to the radial basis functions.

The support of the basis functions are adapted to the grids at each scale and are a function of the ``fill distance'', which measures the sparsity of the grid. Since the basis functions are defined on a compact domain, the system is sparse and computing the solution is fast, especially with the use of iterative methods such as conjugate gradient. As a matter of fact, the complexity of the algorithm solely depends on the number of Voronoï centers and not on the number of selected control points used for motion estimation.

Model estimates motion at several levels of details, from global to local, explicitly taking into account the spatial scales related to turbulence. Figure  displays an example of motion estimation at two different scales from sea surface temperatures measurements in the Black Sea.

The INRIA P3+3 project DESMED has been starting since 2006. It involves the Clime project, CNR in Italy, INSAT in Tunisia, and the Ibn Tofail University in Morocco. The goal of DESMED aims at analyzing long term time-series of vegetation indices acquired by the NOAA-AVHRR sensor, in order to characterize desertification processes occurring in Northern Africa and Southern Italy.

Currently, the achievements of the project are: First, databases have been established for documenting learning sites (Menzel Habib and Jfarra in Tunisia, Salento peninsula in Italy) with classification of Landsat images at different dates, and co-registered time-series of weekly and monthly vegetation indices from 1995 to 2006. Second, definition of a processing chain for characterizing land degradation from NOAA data: this processing chain models time-series of vegetation indices by polynomials, and represents them using a selected set of parameters. The characterization of desertification is then performed in the vector space defined by these parameters. Currently, the work concerns the automatic selection of parameters for distinguishing safe areas and areas undergoing desertification on the basis of pluri-annual time series of vegetation indices.

In the framework of a research contract with the LYNX company, the Clime team analyses the detection and quantification of damages caused to vineyards by hail events. A sequence of SPOT images, acquired before and after the event, is used for detected and measuring changes of vegetation indices and to relate them to production losses. This is an application of great potential interest for insurance companies.

The researches address the following issues:

The Clime team is studying the use of ontologies for documenting complex remote sensing processing chains.

A first objective is to provide end-users with a documentation adapted to their level of expertise and corresponding requirements. A first group of users includes scientists in remote sensing or environmental experts or geologist, etc. They require a step by step execution of the processing chain, in order to analyse and check intermediate results, change parameterisation, etc. On another hand, operational users would prefer a black box with fully automatic execution using sensible default values, etc.

A second objective is to take advantage of the applicability and usability of ontologies: ontologies help for adapting a given processing chain to another site and/or another application; they enable to share knowledge between different users/developers of the processing chain: a change in the processing chain is documented and described by the ontology; they provide means to reason about knowledge, e.g. at the highest level on the processing chain, at the lowest levels, on data and site specific issues.

These objectives have been fulfilled by developing a hiearchical ontology, based on a tree structure, for describing a given processing chain: land degradation monitoring from MODIS data, developed in the context of the ENVIAIR project. We hope that this ontology will help adapting this processing chain to other applications, such as desertification monitoring (DESMED P3+3 project).

Current research is geared at the automatic derivation of ontologies, consistent with the available software components.

This work takes place within the framework of the Egide PAI Plumesat. The greek partners have developped a pixel-based method allowing the characterisation of plume pixels in NOAA-AVHRR data. The present work attempts at solving some remaining problems by use of the turbulent spatial information properties contained in the various channels of the NOAA-AVHRR sensor.

The Microcanonical Multifractal Formalism (MMF) is a theoretical and algorithmic framework allowing the derivation of geometric structures in turbulent acquisition datasets; these geometric structures describe the multifractal hierarchy of transition fronts in the context of Fully Developped Turbulence (FDT). We make use of a fundamental property of MMF about reconstructible systems: the derivation of a synthesized multispectral reduced signal. We use the assumption that the MSM(Most Singular Manifold) computed in the thermal infrared band is directly related to the streamlines of the underlying fluid, so we take this set as the correct reference on the geophysical fluid flow dynamics. Consequently, we want to use the information of the MSMin combination with other spectral bands to provide a spatially-based discrimination method for the determination of plumes. We will use the signal gradient of a function of channels c₂(near infrared) and c₃(middle infrared) to enhance the discrimination between plumes and others bodies taking into account temperature and reflectance information. Let ( c₂, c₃)be a function of the pixel's grey-level values acquired in spectral bands c₂and c₃. We define a synthesized signal pby propagating 's gradient vectors from the MSMcomputed in channel c₅(thermal channel); that is, we use the MMF reconstruction formula in which the gradient information is replaced by 's gradient values :

with:

This formula means that the gradient of is diffused from the set of strongest transitions on the thermal infrared channel. Results are presentend in figure  in the case of the Genoa acquisition dataset.

The subtropical convergence zone is one of the major frontal systems in oceans, and it is the place where specific complex ocean dynamics, algae blooms and upwelling occur. The phenomena are visible on Sea Surface Temperature (SST), cholorophyl alpha (ocean colour) and altmimetry satellite datasets. We begin the study of the ocean dynamics in the subtropical convergence zone using the microcanonical multifractal formalism (MMF), i.e. from the geometric structures associated to singularity exponents derived within the MMF on satellite acquisition datasets. The MMF provides a unified framework for analyzing the dynamics of related events acquired in different oceanographic acquisition datasets. The first phase of the study associated to these data is an experimental phase. We compute the singularity exponents in the different datasets and begin the analysis by studying the Most Singular Manifolds (MSMs) and other geometric structures derived from the singularity exponents. The datasets have different spatial and temporal resolutions. In figure  we show the singularity exponents and the MSM associated to a particular altimetric acquisition. In figure  we show the singularity exponents associated to the chlorophyl concentration and the SST (Sea Surface Temperature), these oceanographic datasets being available at a finer spatial resolution. The observed similarity between the geometric structures associated to exponents of different datasets show that a similar dynamic is under way in the specified zone. We are now exploiting these results to obtain finer characterizations of the ocean dynamics in the subtropical convergence zone.

A. Turiel has worked recently on the empirical estimation of turbulent diffusivity of a passive scalar with an experimental sequence made at Laboratory for Statistical Physics (ENS Paris). From the results, it is possible to define an effective concept of diffusivity associated to apparent advection's depletion at a given scale of observation. These results open a new way of research for the computation of the multi-scale motion field in ocean dynamics. Indeed, oceanographic turbulent data in the Fully Developped Turbulence regime show that, due to discretization, a passive scalar (like sea surface temperature) does not satisfy the conservation equation at the pixel level. Consequently, we start a study on the multi-scale estimation of the motion field in oceanic dynamics; the method is not based on a conservation hypothesis as it is the case in optical flow methods, but using quantities computed from the singularity exponents.

The accurate computation of singularity exponents is a key aspect of the Microcanonical Multifractal Formalism (MMF). The singularity exponents are computed using a wavelet projection of a multifractal measure: the wavelet projection of measure at x= 0and at scale rin is given by:

with wavelet and

Therefore, it is important to understand, both qualitatively and quantitatively, the influence of the wavelet on the computation of the singularity exponent at x= 0.

We study the influence of the wavelet's tail at infinity on the singularity exponent computed at x= 0. Using the Lebesgue density theorem and the analysis of the integral appearing in ( ), we obtain that the local behaviour of the wavelet at x= 0lets the singularity exponent at 0unchanged when r0, as long as (0) 0, but if the wavelet decreases towards infinity according to a power law : when , powers of n₀pop up in the integral which may change the behaviour of 's singularity exponent at 0, when rtend towards 0. This qualitative analysis is the first step towards a mathematical understanding of numerical artefacts appearing in the algorithms implementing the wavelet projection. The second step will consist in computing the quantitative dependance of the wavelet's tail on the singularity exponents.

The objective of this study is to compute the circulation velocity from a sequence of satellite images of Sea Surface Temperature (SST), in order to assimilate it into an oceanographic circulation model.

It is possible to assess velocities from several images by solving a PDE system (conservation equation, regularity) defined using derivatives of the image computed at every pixels. This is not satisfying in the case of oceanographic observations, since a significant part of the observations of the sea surface is occulted by clouds.

We therefore propose a velocity estimation method with a similar principle as data assimilation: the available image data (not occulted by clouds) constitute observations of SST, to be assimilated within a dedicated Image Model, used to describe the evolution of image information. The Image Model implements a simplified version of the transport of temperature by advection and diffusion: the transport is expressed in the 2D image space, source and sink terms being ignored. The state space is defined by the SST and the 2D components of the surface velocity. The latter are assumed constant during the assimilation time window.

Observations of sea surface temperature are assimilated within the Image Model, by minimizing a functional expressing the discrepancy between the modelled and the observed SST, plus an additional second-order div-curl regularization term applied to the retrieved velocity field.

This study is a crucial step towards the formalisation of assimilation techniques for image data. Current research works address the application of this technique to the assimilation of structured image data such as fronts, instead of considering an image as a collection of independent measurements.

This work is performed in cooperation with M. Honnorat and J. Monnier (INRIA team MOISE) in the framework of the ASSIMAGE ACI: an hydrological model based on Saint-Venant equations (state space constituted of water elevation and 2D velocity) is used in a data assimilation framework for flood forecasting.

The practical difficulty lies in access to observation data, especially 2D velocity. We thus applied tracking methodologies on video acquisitions of water flow. This has been performed on the experimental installation of the Fluid Mechanic and Acoustic Laboratory of University of Lyon (LMFA) of river simulation. Trajectories are computed by tracking targets with a maximum correlation matching method. The trajectories are then assimilated in a Lagrangian framework in order to retrieve initial condition and/or parameters in the hydrological model.

The latest generation of satellite sensors dedicated to atmospheric chemistry provide chemical measurements of the lowest layers of the troposphere: MOPITT (Measurement Of Pollution In The Troposphere) and OMI (Ozone Monitoring Instrument) are already operational on NASA platforms, whereas the IASI (Infrared Atmospheric Sounding Interferometer) and GOME-2 (Global Experiment Monitoring Experiment-2) have been launched by ESA in October 2006. All these instruments provide tropospheric columns of selected trace gases (ozone, nitrogen oxydes): the vertical integral in the troposphere of the gas concentration.

The objective of this work is to assess the feasibility of assimilating the 0-6km ozone column, to be provided by IASI, within the regional Chemistry-Transport Model Polyphemus, in view of improving air quality forecast at European scale. This study is led in the contexts of the ESA-EumetSat ``EPS-MetOp Research Annoucement of Opportunity'' (the Clime project being Principal Investigator), and of the TRAQ proposal (TRopospheric composition and Air Quality) for the future ESA tropospheric mission (around 2012), coordinated by KNMI, and comprises two main steps.

The first step is to assess the potential of the 0-6km ozone columns for air quality modelling, i.e. for improving the knowledge of ozone in the atmospheric boundary layer. A Polyphemus simulation for the month of July 2001, extensively validated, serves as reference and allows to conclude that the boundary layer represents a The sensitivity of boundary layer ozone to changes of concentration in the free troposphere is furthermore evaluated to a mean of 25%. This suggests that a better control of free troposphere ozone, to be provided by the satellite instrument, will in turn allow to better control boundary layer ozone.

The second step consists in leading data assimilation experiments. The IASI data not being available yet, a simulation chain has been developed, based on an atmosphere description (Polyphemus concentrations in the 0-5km domain, climatologies above), on the radiative transfer model LBLRTM (AER), on the IASI instrument model (kindly provided by IPSL/SA) and on the IASI operational inversion procedure SA-NN, developed by IPSL/SA. The simulated 0-6km columns have an average 27% error as compared to the reference, which is larger than the expected 20% accuracy of the IASI columns. The simulated data has been assimilated in a perturbated Polyphemus simulation, by means of an Optimal Interpolation procedure. A 5% improvement of boundary layer ozone concentrations has been observed. The next steps will concern the assimilation of the actual IASI data, expected during 2007.

In the image processing area, most of problematics correspond to ill-posed problems (edge detection, segmentation, optical flow estimation, deblurring, ...). A common method used to solve ill-posedness is to regularize solutions by adding smoothing constraints. For example, Tikhonov like approach proposes to minimise a functional measuring the discrepancy between model and solution and constraining the spatial variations of the solution. It is now well known  that the Euler-Lagrange evolution equation associated to this functional corresponds to a diffusion process.

Similar equations are found in the modelling in many physical situations (meteorology, oceanography, air quality, ...), and data assimilation techniques have proven their efficiency for solving them, even when partial and/or indirect observations of state variables are available.

We propose to exploit this property in order to formulate ill-posed image processing problems in a variational data assimilation framework. The research addresses the definition of evolution models for the image information to be retrieved. In a first step this approach is studied for 3D reconstruction from a sequence of 2D observations: we try to reconstruct the evolution of a 3D object from a sequence of 2D image acquisitions. The observations consist of the 2D images, obtained by projection of the 3D space. The evolution model can be as simple as an optical-flow like constraint (transport of grey level over 3D sequence).

The objective is to evaluate the performance of different data assimilation schemes for atmospheric chemistry-transport models (CTM). Contrary to meteorological models, air quality models are non chaotic and the problem is not the control of the initial conditions but of forcing termes. There are recent applications of variational and sequential data assimilation methods based on atmospheric chemistry-transport models, however, comparison studies of the two approaches in the same experimental setting have never been performed mainly due to technical problematics. The recently developed platform Polyphemus (developed by Clime) makes it possible to overcome these technical difficulties for a data assimilation system.

A typical data assimilation system consists of three components, namely data (observation), model (physics), and assimilation algorithms. We adopted object-oriented techniques, such that the developments of the three components are independent from one another. Most of the classical data assimilation schemes for CTMs have been implemented within Polyphemus for comparison studies. The available sequential schemes are Optimal Interpolation (OI), Ensemble Kalman Filter (EnKF), and Reduced Rank Square RooT Kalman filter (RRSQRT). For the variational approach, we have derived the adjoint model for the underlying CTM Polair3D within Polyphemus using automatic differentiation techniques, and the four-dimensional variational assimilation method (4D-Var) is still under testing and will be available in the near future.

For the first application of the data assimilation system, the simple method OI is employed to assess the impact of assimilating EPS troposphere ozone observations. For advanced assimilation methods, say EnKF, RRSQRT, or 4D-Var, one needs the error specifications for CTMs and/or background (a priori) species concentrations. We approximate the model error by perturbing model input data, such as surface emissions, boundary conditions etc. The preliminary results of EnKF and RRSQRT show that the predictions based on assimilated concentrations approach quickly to reference simulations. This is a strong indication that our approximation of model error is not very realistic, and the assimilation suffers from filter divergence.

In summary, we have implemented both classical sequential and variational assimilation methods within Polyphemus platform, and preliminary results are obtained by perturbation methods. For meaningful results, more investigations are needed on (model and background) error modeling for the atmospheric chemistry-transport models.

The aim of this study is to give an objective response concerning the setting up of an optimal monitoring network over France. For this, Polair3D model forced by ECMWF analysis was used to generate a database representing all probable scenarios accident over one year. Spatial interpolation methods and simulated annealing algorithm were used to assess monitoring networks capacity to detect and reproduce the accident situations. One month of database was used to perform the first tests on the inference chain. Several computing tools (parallel distributed) were designed to alleviate the task.

Adjoint modelling and sensitivities computations have benn carried out for the Chernobyl accident. This work has been carried out as a research training period (IMI department of ENPC) for three of the ENPC students (advisor: Marc Bocquet.) This work aimed at building and validating several tools dedicated to sensitivity analysis of activity measurements with respect to many forcing fields, especially sources. A similar work had been carried out in 2004-2005 on the dispersion of mercury [Roustan, Bocquet]. The goal is to demonstrate that such an approach could also be applied on a radionuclide dispersion episode. Most of the work has focused on the computation of adjoint solutions related to wet deposition (the wet scavenging using a Belot or relative humidity parameterization.) In addition to the results obtained for the sensitivity analysis of the Chernobyl accident, this work can be understood as a prelude to inverse modelling of deposited activity.

The reconstruction of the Chernobyl accident source term has been previously carried out using core inventories, but also back and forth confrontations between model simulations and activity concentration or deposited activity measurements. The approach developped in this work is based on inverse modelling techniques. It relies both on the activity concentration measurements and on the adjoint of a chemistry-transport model. The location of the release is assumed to be known, and one is looking for a source term available for long-range transport that depends both on time and altitude. The method relies on the maximum entropy and the mean principle, exploiting source positivity. The inversion results are mainly sensitive to two tuning parameters, a mass scale and the scale of the prior errors in the inversion. To overcome this hardship, we resort to the statistical L-curve method to estimate balanced values for these two parameters. Once this is done, many of the retrieved features of the source are robust within a reasonable range of parameter values. Our results favour the acknowledged three-step scenario, with a strong initial release (26 to 27 April), followed by a weak emission period of four days (28 April - 1 May) and again a release, longer but less intense than the initial one (2 May - 6 May). The retrieved quantities of iodine-131, caesium-134 and caesium-137 that have been released are in good agreement with the latest reported estimations. Yet, a stronger apportionment of the total released activity is ascribed to the first period and less to the third one. Finer chronological details are obtained, such as a sequence of eruptive episodes in the first two days, likely related to the modulation of the boundary layer diurnal cycle. In addition, the first two-day release surges are found to have effectively reached an altitude up to the top of the domain (5000 metres).

In a previous QJRMS two-part paper, new methods to reconstruct the source for an atmospheric tracer at regional scale have been developed. Specifically the Maximum Entropy on the Mean (MEM) method was extended to large (although linear) data assimilation problem. Tests using twin experiments and a limited subset of the data from the European Tracer Experiment [ETEX] were performed. Although temporal reconstruction knowing the location of the source was satisfying, a full 3D reconstruction was still out of reach with real data. In this work, using the MEM method and some of its refinements, a reconstruction using all ETEX-I measurements at a resolution of 1.125° x 1.125° x 1 hour is shown to be possible. This allows for a reconstruction of the full dispersion event. The MEM retrieval of the tracer plume using what is believed to be a good prior is then compared to other priors including Gaussian ones. Eventually, a reconstruction using all data sequentially in time (not all together) is obtained. This helps define what a maximum entropy filter applied to sequential data assimilation of a linear tracer should be able to do, with a view to an efficient emergency response in case of an accidental release of pollutant.

Source retrieval is one of the problems that are currently being addressed within a framework of data assimilation for dispersion of radionuclides. Firstly, a series of hypothetical releases have been designed. The accidents have been imagined to take place at one of the European nuclear facilities at a time. The aim of a retrieval is to tell the position of the source and the shape of its temporal profile. The solution is given by a procedure based on the maximum of entropy principle. A couple of new, problem-adapted cost functions have been put forward and their performance tested. The tests have been undertaken with perfect and noisy synthetic measurements, and have been assessed with an objective indicator. In perfect measurement configurations, perfect reconstructions have been obtained for a number of measurements significantly lower than the number of unknowns. Secondly, temporal profile of an accidental release of caesium-137 in Algeciras steel mill has been inverted. The total reconstructed activity falls within an interval given by the official estimations. The profile is narrow which remains in accordance with the information disclosed after the release but is slightly shifted towards the earlier times.

A strong limitation of chemistry-transport models lies in the high uncertainties in the physical parameterizations and the input data (meteorological data, emissions, ...). Uncertainties in input fields often range between 20% and 50%. Many physical parameterizations are available to estimate the same fields, which is usually the main source of uncertainties in output concentrations. In this context, a single forecast has little meaning: modern forecasting systems should plan to include ensemble forecasts, that is, simulations from an ensemble of models.

The modeling system Polyphemus has been designed in order to handle ensembles: it hosts several chemistry-transport models and includes many options with regard to the physical formulation of the models. An ensemble of 48 models has been studied to apply ensemble methods to photochemical forecasts (ozone). Methods have been proposed to build a forecast with linear combinations of the models outputs. Significant improvements in forecasts are obtained when the combination weights are optimal in least-square sense over the past (moving learning period).

On top of all models and of several model combinations, machine learning algorithms (sequential aggregation) have proven to improve performances. Unlike other methods, they come with theoretical bounds and are well known for their robustness. This is joint work with Gilles Stoltz (ENS Paris, DMA).

Ensemble forecasts (without combinations) have been tested daily (and for months) for the operational forecasting platform Prév'air ( http://www.prevair.org/).