Centre d'Enseignement et de Recherche en Environnement Atmosphérique

Laboratoire Commun

École des Ponts ParisTech - EDF R&D

EDF

Inverse modelling, data assimilation group

Moderator: Marc Bocquet


This group is also part of the ENPC / INRIA project : CLIME.
The main topics we are working on are Below are listed several examples of our contributions...

Inverse modelling of NOx emissions at regional scale with a variational approach

(Denis Quélo, Vivien Mallet, Bruno Sportisse)

Emission inventories are usually recognised as highly uncertain. The uncertainties range from 30% to 50% depending on the pollutants and affect in particular the temporal distribution. A case study of inverse modelling of emissions at regional scale for photochemical applications has been performed on the region of Lille in the Northern France using measurements of ozone and nitrogen oxides in May 1998. It has been shown that inverse modelling of the time distribution of nitrogen oxides emissions leads to satisfactory improvements of ozone and NOx forecasts even after the learning period.

NOx profiles
Optimised time distributions of NOx emissions over different periods.

References:

  1. Inverse modeling of NOx emissions at regional scale over Northern France. Preliminary investigation of the second-order sensitivity
    Denis Quélo, Vivien Mallet and B. Sportisse,  2005, J. Geophys. Res.
  2. Data assimilation for air quality modeling.
    Denis Quélo, 2004, PhD Ecole Nationale des Ponts et Chaussées

Inverse modelling for near-field dispersion problem

(Monika Krysta, Marc Bocquet, Bruno Sportisse, Olivier Isnard)

Data assimilation for a near-field dispersion problem makes use of standard variational approach based on an adjoint formulation. It addresses:

Physical modelling is performed with a Gaussian puff model, pX 0.1. The model is based on analytic solutions to the advection-diffusion equation. It has been developed by IRSN French Institute of Radiation Protection and Nuclear Safety. An adjoint of pX 0.1 has been built in CEREA. It is flexible enough to optimise instantaneous or mean variables as required. Data assimilation tests have been performed on wind tunnel measurements which are essentially mean activity concentrations. wind tunnel scale model
Scale model of Bugey nuclear power station used in a wind tunnel experiment

Results :


References:

  1. Data Assimilation for Short-range Dispersion of Radionuclides: an Application to Wind Tunnel Data
    Monika Krysta, Marc Bocquet, Bruno Sportisse, Olivier Isnard, in press, Atmospheric Environment, 2006

Inverse modelling for continental scale dispersion

(Monika Krysta, Marc Bocquet)

Model-measurement coupling problem at continental scale has been focussed on source inversion:

Maximum entropy principle-based method has been employed to reconstruct sources. A series of OSSEs [Observing System Simulation Experiment] and an inversion of a real accident have been conducted. Synthetic experiments use a list of all nuclear facilities in Europe and a restricted network of radioactivity monitoring stations. Several accidental releases have been devised, simulated with Polair3D and inverted on the basis of synthetic measurements. Prior information referring to boundedness of the accidental source as well as its spatial and temporal confinement let us put forward problem-adapted cost functions. We have replaced the delocalised source cost function with localised and point-wise ones according to the needs. A score (statistical indicator) has been used to evaluate the performance of the algorithm. Results:


Reference:

  1. Source reconstruction of an accidental radionuclide release at European scale
    Monika Krysta and Marc Bocquet, submitted to QJRMS, 2006.

Inverse modelling of an atmospheric tracer at continental scale

(Marc Bocquet)

etex1-3D

High-resolution reconstruction of the ETEX-I source using perturbed (20%) synthetic measurements at 1°x1°x1h. The map represents the PMCH concentration field integrated in time for each space grid-cell. This work aims at defining extended or new methods for the reconstruction of the source a passive tracer (or least that behaves linearly). This source could be extended or even diffuse but the emphasis is on accidental release of pollutant for which sources are localised in space. The resolution is intended to be high (O.5x0.5x1h) so that the related inverse problem is usually ill-conditioned (if not ill-posed). The set of methods which have been developed are extensions of the maximum entropy on the mean principle to large data assimilation problems (in several respects: high number of constraints, efficient handling of the background information)


References:

  1. Reconstruction of an atmospheric tracer source using the principle of maximum entropy. I: Theory
    Marc Bocquet, Quarterly Journal of the Royal Meteorological Society, 131, part B (610), p. 2191 (2005).
  2. Reconstruction of an atmospheric tracer source using the principle of maximum entropy. II: Applications.
    Marc Bocquet, Quarterly Journal of the Royal Meteorological Society, 131, part B (610), p. 2209 (2005).

Grid-resolution dependence in the source reconstruction

(Marc Bocquet)

several resolutions

Examples of ETEX-1 source inverse modelling when the space resolution of the reconstructed object is changed. There is failure in the reconstruction when the resolution is too fine. These maps correspond to maps of reconstructed sources integrated in time for resolutions 0.5°x0.5°, 1°x1°, 2°x2°, and 4°x4°.

The reconstructed source of a linear tracer obtained through inverse modelling depends directly (though not only) on the resolution chosen for the source. Roughly speaking, the resolution should match the information given by the observations and the prior knowledge on the source. Yet, this balance is difficult to strike. Besides, it has been observed by J.-P. Issartel, former member of the CEREA, then proven by M. Bocquet that past this balance and as the resolution gets finer, the reconstruction starts to fail. It was shown that, in this context, a solution is obtained which is weak in magnitude and concentrated near the observation stations. This has been proven analytically in the Gaussian hypotheses case. This was then quantified in the general non-Gaussian cases, using a rigorous mathematical indicator, which is a ratio of entropies.


Reference:

  1. Grid resolution dependence in the reconstruction of an atmospheric tracer source.
    Marc Bocquet, Nonlinear Processes in Geophysics, 12, p. 219-234 (2005).

Sensitivity analysis for mercury over Europe

(Yelva Roustan, Marc Bocquet)

A chemical mechanism devoted to atmospheric mercury has been implemented to model its fate and transport over Europe. Adjoint techniques, relying on the linearity in the species concentrations of the model, have been developed to perform sensitivity analysis for an area limited domain. These techniques allow to quantify in a convenient way the different contributions to a given modeled measurement. Because of the backward point of view (specific to adjoint methods), sensitivities of this measurement with respect to emissions, boundary conditions and initial conditions can be obtained in a single run. The modeled measurement may typically be an air concentration but also a dry, a wet or a total deposition flux. Its spatial and temporal definition allow for different applications. An especially interesting one concerns transboundaries pollution issues.


sensitivities
Sensitivity to emissions of the mercury annual average modeled air concentration measurement. Application to transboundaries pollution issues for Germany (a), France (b) and the Czech Republic (c). In the case of the Czech Republic examples of monthly averaged sensitivities are also given to demonstrate the intra-year variability of the sensitivity ((d), (e) and (f)).

Reference:

  1. Sensitivity analysis for mercury over Europe.
    Roustan Y. and Bocquet M., 2006, Journal of Geophysical Research, Vol. 111, D14304

Inverse modelling for mercury over Europe

(Yelva Roustan, Marc Bocquet)

The sensitivity analysis previously performed reveals the appreciable influence of the boundary conditions on the modeled ground measurement of gaseous mercury. Inverse modelling can help to constrain the forcing fields and then help to improve the predicted mercury concentrations. The adjoint solutions computed to carry out the sensitivity analysis relate explicitly the modeled measurements to the forcing fields. They may be employed to perform the inversion of the boundary conditions. Several inversions are made, with a simple chemical mechanism and a more complex one, taking into account or not the intra-annual variability of the boundary conditions.
retro_new
Monthly averaged ground measurement of gaseous mercury (in ng.m-3) at four EMEP sites for the year 2001. The observations data of the first two stations are used for the assimilation process.

The inverse modelling of the boundary conditions give interesting results. However inverse modelling of mercury emissions is much more difficult due to the small number of monitoring stations.


Reference:

  1. Inverse modelling for mercury over Europe
    Roustan Yelva and Marc Bocquet, Atmos. Chem. Phys., 6, 1-14, 2006

Data assimilation for air quality forecast (part of INRIA's ADOQA project)

(Lin Wu, Vivien Mallet, Marc Bocquet, Bruno Sportisse)

The objective is to evaluate the performance of different data assimilation schemes for atmospheric chemistry-transport models (CTM). Due to the highly-nonlinear and non-chaotic nature of the CTMs, the conclusion of this comparison study is not obvious. The software structure of Polyphemus, a platform for air quality modeling, makes it possible to implement and compare diverse data assimilation methods in the same experimental settings. Both sequential and variational methods are under investigations. Preliminary codes for EnKF and RRSQRT are ready, and we are now working on the 4D-Var schemes. Comparison results will be at hand in the near future. The following figures are reference ozone concentrations over Europe, and the assimilation results of EnKF and RRSQRT.


reference run
 enkf
rrsqrt





Top-left: Reference run.
Top-right: Assimilation results using EnKF.
Bottom-left: Assimilation results using RRSQRT.