Mireille Garreau

Marie-Paule Garcia

François Tavard

Antoine Simon

Julien Fleureau

Jérôme Velut

Dominique Boulmier

Pascal Haigron

Christine Toumoulin

Christophe Leclerc

Christophe Leclercq

Abilities of cardiac MSCT imaging to provide useful anatomical and functional information for Cardiac Resynchronization Therapy optimization

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Cardiac Resynchronization Therapy (CRT) has been shown to improve cardiovascular function and reduce mortality rates in a specific subpopulation of patients suffering from heart failure [1]. However, about 1/3 of the patients implanted do not respond appropriately to this therapy [START_REF] Mehra | Cardiac resynchronization therapy: caveat medicus![END_REF]. One way to decrease this non-response rate would be to optimize candidate selection in CRT and device implantation strategy [START_REF] Chung | Results of the Predictors of Response to CRT (PROSPECT)[END_REF]. One of challenging tasks to carry out remains both the identification of the most effective pacing sites and the left ventricular lead positioning (by a venous access). This topic is a real challenge and is the purpose of active actual research works [ref publis issues euheart].

This work is part of the IMOP project (IMaging for Optimisation of biventricular Pacing) which purpose is to define a CRT optimization method based on the fusion of mechanical, electrical and anatomical data.

Multislice

Computed Tomography (MSCT), combining ultra-fast rotating gantries, multi-rows detectors and retrospective ECG-gated reconstruction, provides datasets representing the whole cardiac cycle with a high spatial resolution. It enables to provide an anatomical description of cardiac structures (ventricles and coronary vessels) but also a functional description, both obtained in one single examination. With this modality, transvenous path finding methods [START_REF] Coatrieux | Transvenous path finding in cardiac resynchronization therapy[END_REF], anatomical structures extraction methods [START_REF] Ecabert | Automatic modelbased segmentation of the heart in CT images[END_REF][START_REF] Larrabide | GIMIAS: An Open Source Framework for Efficient Development of Research Tools and Clinical Prototypes[END_REF] and motion estimation approaches have been previously proposed [START_REF] Simon | A surface-volume matching process using a Markov random field model for cardiac motion extraction in MSCT imaging[END_REF].

Our objective is to better plan the placement of CRT leads using the MSCT capabilities in imaging the heart. This paper aims to show how cardiac CT imaging can be helpful for the clinician to analyse both venous system and cardiac function before the device implantation. This paper is organized as follows: a synthetic description of the different processing steps involved in the global approach is firstly given, including a vessel tracking and characterization process, the 3D LV shape segmentation and motion estimation, the extraction of motion parameters and the fusion and visualization of all available information. Some of these steps have been previously proposed. Results obtained on two patient databases are presented and discussed in a qualitative and quantitative way, and followed by some conclusions.

Methods

The proposed process is decomposed in four steps: (1) the 3D tracking of coronary veins based on fast-marching techniques; (2) the 3D LV extraction along the cardiac cycle by using a fuzzy connectedness algorithm; (3) the cardiac LV motion estimation based on a multi-resolution surface matching method, giving access to functional parameters associated to anatomical segments; (4) the fusion of extracted data with adapted modes of visualization.

2.1.

Vessel Tracking and Characterization

This section introduces the implemented method for extracting and characterizing the coronary veins from MSCT volumes. The proposed tracking procedure is based on minimum-cost path computation and makes use of `Fast-Marching' technique. The algorithm aims at propagating a front inside curved tubular structures of varying width and yields a first estimation of the vessel axis. This first path is then used to give an accurate estimation of the local features of the vessel, that is, a centered position on the vessel axis and its corresponding radius.

An efficient way to solve the minimal path problem in 3D images is the `Fast-Marching' procedure [START_REF] Deschamps | Fast extraction of minimal paths in 3D images and applications to virtual endoscopy[END_REF]. The `Fast-Marching' algorithm describes a front propagation scenario, which progresses outward from an initial point P0 (fig 1). This front passes only once over a voxel and compute a map to deduce the minimum cost path by backtracking when the final point PF is reached by the front. The value associated to a point P on the previous map represents the cumulative cost of its minimum cost path from P0.

Figure 1. Front propagation principle in 2D space: the front propagates into the vessel lumen from the point P0, guided by the vessel local orientation. In dark blue, points whose cumulative cost of the minimal cost path from P0 is computed. In light blue, positions where the front is definitely stopped thanks to the Freezing procedure.

To cope with contrast inhomogeneities and lowcontrast environment, Garcia et al. [START_REF] Garcia | Coronary vein tracking from msct using a minimum cost path approach[END_REF] proposed a front propagation procedure with orientation constraint. In this approach, the front is not allowed to propagate beyond vessel boundaries. To achieve this goal, the front propagation is guided by a specific cost function which considers the reciprocal of a vesselness measure weighted by the orientation information. Local orientation and vesselness measure are computed from the eigenvalue analysis of the Hessian matrix and Frangi's filter [START_REF] Frangi | Multiscale vessel enhancement filtering[END_REF]. The front evolves fastest in the direction of the vessel local orientation and in regions where the vesselness measure is higher (close to the vessel axis). The front is definitely stopped at non-vascular positions and at positions where the propagation direction is too different from the vessel local orientation. However, in case of low-contrast zones, the previous positions may not be assigned a strong enough value to definitely stop the front. Thus, while the front progresses in the vessel, a Freezing procedure is needed to definitely stop the front at those positions [START_REF] Cohen | Segmentation of 3d tubular objects with adaptive front propagation and minimal tree extraction for 3d medical imaging[END_REF].

Finally, this extracted centreline corresponding to the resulting minimum cost path is used to locally characterize the vessel thanks to geometrical moment computation [START_REF] Boldak | An improved model-based vessel tracking algorithm with application to computed tomography angiography[END_REF]. Thus, a correction of the estimated centered position and its corresponding radius are computed.

The previous tracking procedure [START_REF] Garcia | Coronary vein tracking from msct using a minimum cost path approach[END_REF] was assessed on synthetic and real data sets. A parametric study was performed on a synthetic data set representing coronary veins with similar features to those of MSCT volumes. Furthermore, a qualitative evaluation on coronary veins labelled and classified according to their visibility on MSCT volumes was performed (expertized by a cardiologist). The method appears robust to contrast inhomogeneities in MSCT volumes [START_REF] Garcia | Coronary vein tracking from msct using a minimum cost path approach[END_REF].

4D LV segmentation

The segmentation of the left cavities, along the whole cardiac cycle, is based on a fuzzy connectedness algorithm [START_REF] Fleureau | Assessment of global cardiac function in MSCT imaging using fuzzy connectedness segmentation[END_REF]: from a seed point (chosen interactively), it generates a connectedness map, associating each voxel to the seed. The connectedness is based on affinity (measuring the similarity, in terms of intensity and spatial distance, between voxels and the seed) and path (linking voxels to the seed). Considering this Dijkstra algorithm, the construction of the connectedness map has been realized with low costs in terms of memory use and rapidity [START_REF] Simon | Cardiac Motion Extraction Using 3D Surface Matching in Multislice Computed Tomography[END_REF]. This algorithm begins from a central seed point in the object of interest and expands the research in the graph in a width way.

An extension in time of this process has been realized in order to study the global cardiac function. For that purpose, the connectedness segmentation algorithm is applied on dynamic CT datasets. Considering that the left cavity is not submitted to a large global displacement, the same seed point can be used for all the 3D volumes of one patient database, provided that this point is positioned about the centre of the cavity. From this seed point, the left cavities are segmented along the whole cardiac cycle.

The surface reconstruction of the segmented volumes is then realized using Marching Cubes algorithm and resulting to surface meshes representing the left cavities (left ventricle and auricle, beginning of the aorta). The final step is to cut through the reconstructed surface in order to extract the left ventricle. This is based on the semi-automatic placement of a 3D plane at the valvular plane at the first time-instant of the sequence. The selected plane is used to cut through the surface and to initialize the same process at the following time.

This method therefore gives access, with few interactions, to the evolution of the cardiac volume along the whole cardiac cycle. Results have been compared to measures made during clinical routine with MSCT and MRI (only at end-diastolic and end-systolic phases) and have provided satisfying results (volume difference less than 10%).

Cardiac motion estimation and characterization

Once the previous step provides the segmentation of the left endocardium along the whole temporal sequence and the reconstruction of the surface meshes corresponding to the segmented surfaces, the motion estimation step is applied. This last method we have previously proposed [START_REF] Simon | Cardiac Motion Extraction Using 3D Surface Matching in Multislice Computed Tomography[END_REF][START_REF] Garreau | Surface and motion extraction in cardiac MSCT imaging for the assessment of left ventricular function[END_REF] relies on the temporal surface matching to estimate the displacements of the mesh nodes.

The motion estimation relies on the multi-resolution matching of each pair of surfaces (S1, S2) corresponding to two following instants of the cardiac cycle. It is based on the definition of a Markov Random Field F, whose sites are the nodes of S1 and labels are the nodes of S2. The most probable realization of F, according to a global energy U, leads to the estimated motion field. The matching is guided by mean and Gaussian curvatures. In order to take advantage of the spatiotemporal regularity of the motion field, the energy U includes terms privileging low amplitude and spatially regular displacements. A multi-resolution scheme is used in order to optimize the minimization process. At the lowest resolution, the energy minimization is performed using a simulated annealing algorithm while, at higher resolutions, an iterated conditional mode (ICM) algorithm is used.

The application of this method to each pair of successive surfaces S1 and S2 results to one motion field associated to each instant of the cardiac cycle and defined on the set of nodes of the corresponding endocardial mesh. From the obtained motion fields, motion descriptors can be extracted. For instance, maximal displacement (according to the first time-instant of the sequence at end-diastolic phase), time-instant corresponding to this maximal displacement and total displacement can be computed. Complementary works have been also proposed to extract different motion components of functional parameters such as radial and longitudinal motion components [START_REF] Garreau | Surface and motion extraction in cardiac MSCT imaging for the assessment of left ventricular function[END_REF].

This technique has been evaluated on simulated data and on real data, with comparison of global extracted motion parameters measured on clinical stations with CT and MRI modalities. A work has been developed to compare motion components measured from CT and from ultrasound Speckle Tracking Imaging and have provided coherent measures between these modalities, in particular for longitudinal displacements [START_REF] Delaunay | Cardiac Function Estimation for Resynchronization Therapy: Comparison between Multislice-CT and Speeckle Tracking Imaging[END_REF].

Data visualization

Different modes of visualization can be chosen and adapted according to the clinician needs for CRT optimization. If we consider help for gesture planning, it is of interest to visualize the veins that are present, their diameter and orientation with a global 3D representation of the venous network but also with a precise delineation of veins in curvilinear planes to see clearly the neighboring structures. Motion extracted parameters can then be displayed using different representation modes, e.g. 3D endocardial surface for a precise description or bull-eye representation based on the 17 cardiac anatomical segments. Of course, the fusion of vessels with color-codes surfaces describing LV motion extracted parameters in superposition with extracted cardiac left structures (endocardium, auricle) can be helpful to better precise the site for CRT lead placement.

Results

These methods have been applied to three patient data (selected patients for CRT with severe asynchronism). The algorithms have been applied on MSCT data sets acquired with a MSCT scanner (General Electric Healthcare LightSpeed VCT 64-slice Scanner) providing 20 3D reconstructed volumes by ECG postsynchronization (resolution: 0.3x0.3x0.5 mm) representing a whole cardiac cycle. A preliminary interpolation was performed to make the datasets isotropic.

Results obtained on two patient databases are shown (identified as cases P1 and P2). About vessel extraction, coronary venous tree was better contrasted from the 50% volume to the 80% volume of the sequence. For case P1, five veins have been extracted with the vessel tracking process included the Coronary Sinus (CS), the Mean Vein (MV), the Great Cardiac Vein (GVC), the Postero-Lateral Vein (VPL), the Lateral Vein (VL). For case P2, five veins have been extracted with SC, MV, GVC, VPL and Antero-Lateral Vein (AVL) (fig. 2).

Conlusion

4D CT data have been analyzed in order to extract global and local left ventricle (LV) function and coronary vein anatomy. The integration of the overall set of available information with adapted modes of visualization may represent an advance towards the optimal use of CT imaging in CRT planning. This approach has been tested on three patients. First results show that combined anatomical and functional information, concerning in particular the characterization of the venous network and the LV local motion, are of interest for CRT optimization. This work is associated to other works providing the means to combine multimodal information describing anatomical, but also functional and electrical data [START_REF] Tavard | Data fusion of left ventricle electroanatomical mapping and multislice computerized tomography[END_REF]. A complete validation of these methods has to be realized with a great number of candidate patients for CRT.

Figure 3 .

 3 ajout fig cas 04 et rogner pour être plus grand Figure 3. 3D representation of extracted venous networks : (a) case P1 (SC, MV, GVC, VPL, VL veins), (b) case P2 (SC, MV, GVC, VPL, AVL veins) Examples of extracted coronary veins are given on curvilinear reconstructed slices for the two patients on figure 3. These images display in blue color the extraction of the Great Cardiac Vein (a) for case P1 and the Antero-Lateral Vein (b) for case P2 with respective diameter interval of 1.8-2.8 mm and XX-XX mm. These veins have been selected for the left ventricular lead placement during the CRT gesture. Examples of extracted coronary veins with their diameter on curvilinear reconstructions: (a) case P1, Great Cardiac Vein; (b) case P2, Antero-Lateral VeinThe segmentation process allowed the extraction of the left cavities and in particular the left ventricle endocardium. The LV mesh surfaces have then be used to estimate the motion along the cardiac cycle, providing the means to extract global and local motion parameters. For each patient P1 and P2, a representation of the fusion of both extracted venous network and measured local maximal displacement is displayed with their superposition on the 3D extracted cardiac surfaces (fig.4, 5). This combined data visualization allows to associate specific dynamic behaviour of anatomical regions to their vein vessels and to better identify a site of interest.XXX compléterModif à faire : 2 incidences si possible et + gros

Figure 4 .

 4 Figure 4. Case P1: Representation of venous network (in dark red color) and extracted local cardiac function: maximal displacement (mm) represented in color with a 3D surface (left oblique anterior view) (left) -(right anterior view (right)

Acknowledgements

This work is supported by the French National Research Agency (n°04 T 187 -188 -189 -190 CITH and n°ANR-07-EMPB-007-01) and the Brittany Regional Council.


Charles Raux
email: charles.raux@let.ish-lyon.cnrs.fr

Grégoire Marlot

A system of tradable CO 2 permits applied to fuel consumption by motorists

Keywords: D120, D450, R410, R480 transferable permits, transport, greenhouse gas, surplus

Decentralized transferable permit systems in the transport sector can be of interest with regard to reducing greenhouse gas emissions, in spite of anticipated transaction costs. This paper describes a potential application of a domestic market for car fuel consumption permits. The marginal costs of consumption reduction vary sufficiently according to motorists' residential locations to consider permit exchanges. Economic evaluation of this system shows that there are transfers of surplus between the various groups of motorists according to their residential locations. The central government may lose significant revenues when compared with a conventional fuel tax. Lastly, the issue of transaction costs, the benefits and disadvantages in terms of social acceptability and equity are discussed.

Introduction

At the 1992 Rio Earth Summit and the 1997 Kyoto Conference, the majority of developed countries accepted the creation of legally binding quotas for greenhouse gas emissions (GHGs) with the aim of stabilizing the atmospheric concentration of these gases. The transport sector is one of the main sources of GHGs, and the principal source if we only consider CO 2 (the transport sector was responsible for 34% of French CO 2 emissions in 1999, and 30% of the CO 2 emissions in the USA in 1997). In addition, the transport sector has one of the highest potentials for further GHG emission increases.

According to an OECD study, the share of GHG emissions from transport could increase from 25% in 1995 to 30% in 2020 (OECD, 2000a).

Studies of transport emission reduction strategies (see for instance OECD, 2000b) have all agreed that the foreseeable improvement in car technology is inadequate, within the 20 year time horizon, for countries to meet the Kyoto or Rio objectives. These studies also emphasize the need for approaches that combine technological, economic and social aspects. These "packages" of measures should include a variety of policies for limiting vehicle-kilometres travelled by providing alternatives to the private car, by combating urban sprawl, by increasing public awareness, but also by means of economic instruments such as taxation or transferable permits.

As we shall go on to explain, fuel taxation has limits with regard to efficiency and social acceptability. For this reason, it is worthwhile considering transferable permits as an alternative means for countries to attain their GHG emission level objectives.

The economic theory behind pollution permit markets can be traced back to the work of [START_REF] Coase | The problem of Social Cost[END_REF] on external costs, followed by that of [START_REF] Dales | Land, water and ownership[END_REF] on regulating water use, and the formalization of pollution permit markets by [START_REF] Montgomery | Markets and licenses and efficient pollution control programs[END_REF]. According to Godard's general definition (in OECD, 2001), transferable permits are a variety of instruments ranging from the introduction of flexibility into conventional regulation to the organization of competitive permit markets. These instruments share the following common features: (1) they involve the fixing of quantified constraints (quotas); (2) these quotas (or rights) are initially allocated to agents independently of the environmental obligations imposed on them; (3) agents are authorized to transfer these quotas between different activities or different places (averaging), between different periods of time (banking) or to other agents (trading); (4) ad hoc penalties are applied to ensure that agents only emit the equivalent of those rights or quotas which they hold.

However, it is generally considered that the large number of moving emission sources which characterize transport constitutes an insurmountable obstacle to the introduction of emission permit markets within this sector. Thus, the only economically efficient response would involve extension of current fuel taxation to include a kind of "CO 2 tax". The aim of this paper is to explain briefly what advantages a decentralized transferable permit system in the transport sector has over traditional taxation and to show how a permit system as an alternative to a CO 2 tax could work. The case of France is used as an example for practical application.

The first section will discuss the limits of taxation and outline the potential advantages of permit markets in the transport sector. The second section describes a decentralized permit system for motorists: it includes the principles and practical implementation, the socioeconomic evaluation in the French case, and finally equity and acceptability issues.

The limits of taxation and the potential of transferable permits

The instrument of taxation is widely used in the transport sector, essentially because of its tax yield. Excise duties levied in the European Union in 2002 varied in member states from €0.296 to €0.742 per litre for premium grade petrol and from €0.242 to €0.742 per litre for diesel oil (Commission of the European Communities, 2002). In France, fuel excise duties provided the central government with bn€27 in 2002 for a GDP of bn€1,522. Although the current level of taxation might be considered high, it is not high enough to reduce road fuel consumption. The level of taxation required to reduce CO 2 emissions can be estimated from the price elasticity of fuel demand1 , whose value varies depending on whether short-term or long-term effects are taken into account. This is because, in the event of an increase in fuel price, some adaptations such as changes in driving style, reducing or optimizing some trips, or changing transport mode can be implemented in the short-term (for example, in the weeks or the months which follow the price increase). Other adaptations, such as changing one's vehicle, residential location or place of work, take longer. Price elasticity values vary between -0.3 for the short-term and -0.7 for the long-term [START_REF] Goodwin | Evidence on car and public transport demand elasticities 1980-1988[END_REF]. This is ordinary elasticity, related to a marshallian (or non-compensated) demand function, which therefore includes the substitution and income effects.

We can obtain some orders of magnitude by applying a few figures to the case of France. With a price elasticity of -0.7, a fuel cost of €1.06 /l (as in February 2000) and the objective of reducing consumption by 10%, the price would need to rise by 14%; i.e. an additional €0.15/l of tax. As a result of a large increase in the price of crude, the price paid by the consumer for premium grade petrol increased by 17% (from €0.9 to €1.06) between February 1999 and February 2000. In view of the short-term elasticity, fuel consumption and traffic should have been affected immediately. However, the two parameters continued to rise in 1999 and only stabilized in 2000 before rising again in 2001 [START_REF] Urf | Faits et Chiffres. Statistiques du transport en France[END_REF]. We can perceive here the effect of the sustained economic growth observed at the end of the 1990s. The amount of tax required to reduce GHG emissions should also therefore take account of the income elasticity of fuel demand, which is positive. In other terms, in order to remain effective in moderating fuel consumption, the tax on fuels should increase at the same rate as the economy grows.

Furthermore, variations in the price of petrol are likely to cancel out the effect of this tax on the end consumer. The turnaround in the oil market that took place in 2001 essentially cancelled out the 1999-2000 price rise, as the price of premium grade unleaded petrol returned to a little under €1 (the usual level in 2002 and 2003): the price effects of a CO 2 tax would have been wiped out.

Lastly, the "tax rebellion" that took place in several European countries in September 2000 shows how sensitive public opinion is to fuel taxation (Lyons and Chatterjee, 2002). Central government is a focus for opposition as it benefits from the tax, although it has little control over oil prices.

Thus, not only do fluctuations in oil prices mean that the effectiveness of a tax is extremely unpredictable, it is also not at all sure that it would be accepted by public opinion. Both these factors encourage us to explore the feasibility of CO 2 emission permits in the transport sector.

Theoretical and practical knowledge and the potential for transferable permits in the transport sector have been analyzed by [START_REF] Raux | The use of transferable permits in transport policy[END_REF]. For transport, transferable permits have some interesting features when compared with taxation:

• The price response function of agents is affected by a non-negligible degree of uncertainty. Furthermore, the price elasticity of fuel demand is low in the short or medium term: a quantitative objective would be easier to achieve with the permit system than with taxation. • In view of the high level of fuel taxation in Europe, freely allocated permits would be seen by agents as a means of escaping an additional tax, possibly making the new instrument more acceptable. • Quota systems are the only systems which allow distributive aspects to be treated in an explicit manner, independently from the issue of the economically efficient allocation of efforts to reduce environmental damage: in view of the fundamental role of transport as regards access to activities and locations, particular attention must be given to these distributive impacts. • When transferable permits are applied to GHG emissions from transport it is possible to fix precise quantitative objectives for each agent, as overall output is equal to the sum of agents' individual outputs; at planetary level it matters little where GHGs are emitted, and the quotas can be exchanged within a domestic or even planetary geographical area.

A system of transferable permits equalizes the marginal costs of reduction between all emission sources. Under certain assumptions this is a sufficient condition for minimizing the cost of achieving a given emissions reduction objective [START_REF] Baumol | The theory of environmental policy[END_REF]. This result is obtained independently of the initial allowance of the rights, which makes it possible to separate the questions of efficiency and equity. However, [START_REF] Stavins | Transaction costs and tradable permits[END_REF] has shown that when transaction costs are involved -the search for partners for the exchange, negotiation, decision-making, follow-up and compliance with the rules -the initial allocation of rights affects the final balance and the total cost of reducing emissions. The authorities may therefore attempt to reduce these transaction costs, for example by avoiding finicky regulations or by facilitating the activity of intermediaries between vendors and purchasers [START_REF] Hahn | Marketable permits: lessons for theory and practice[END_REF][START_REF] Foster | Designing more efficient markets: lessons from Los Angeles Smog Control[END_REF].

An economic incentive instrument achieves its maximum efficiency when it operates at the most decentralized level possible. This why we do not deal further with the option of "upstream" permits where the permits would be allocated to fossil fuel producers and importers [START_REF] Winkelman | Transportation and domestic greenhouse gas emission trading[END_REF]. The transmission of permit prices by these fuel wholesalers to final consumers would lose the advantages of permits over tax referred to above, without forgetting the issue of acceptability of letting private companies manage the fuel rationing.

This issue of administrative costs is the main argument against the use of permit systems within the transport sector which, by definition, involves a large number of mobile sources. Perhaps this explains why the only application or propositions in the literature are confined to systems targeting auto makers and concerning unitary vehicle emissions (for example, [START_REF] Albrecht | The diffusion of cleaner vehicles in CO2 emission trading designs[END_REF][START_REF] Wang | Cost savings of using a marketable permit system for regulating light duty vehicle emissions[END_REF]and the ZEV programme in [START_REF] Raux | The use of transferable permits in transport policy[END_REF]. The main advantage of these proposals is that the permit systems would involve a small number of participants thus allowing minimum transaction costs. Permits on household car ownership are another indirect way of controlling car travel [START_REF] Walton | The potential scope for the application of pollution permits to reducing car ownership in the UK[END_REF] but the linkage with actual fuel consumption is very crude. These systems have the disadvantage of ignoring the other component of total emissions, fuel consumption through actual vehicle use by drivers.

Controlling land use [START_REF] Ottensmann | Market-based exchanges of rights within a system of performance zoning[END_REF] is in principle an attractive way of reducing distances traveled, but it is controversial -it has still not been proven that it is possible to reverse the tendency to travel longer distances by compacting locations again. However, alternatively, the spatial concentration of activities yields more opportunities for cost-efficient transport alternatives, such as mass transit, that are less energy consuming.

Other ideas circulate, encompassing all fossil fuel consumption and not just car fuel: according to these proposals a "carbon allowance" should be given on a per capita basis. The most elaborated proposal is "domestic tradable quotas" by [START_REF] Fleming | Stopping the traffic[END_REF] which would be allocated partly free to adults and partly by tender to firms and other economic agents. To our knowledge this proposal is still under study and the practical implementation including technical, institutional and equity aspects has not yet been devised. While the idea of "carbon allowance" is attractive, one suspects that its application to every aspect of household energy consumption needs careful investigation and assessment of each one separately, e.g. home heating and family use of energy, transportation and so on. This is why the following section of the paper proposes and discusses a system of tradable permits on the demand side which targets decisions of motorists regarding their fuel consumption. The main challenge here is to reduce the administrative costs of such a system as much as possible. Such a system would come not as an alternative but as an addition to other systems on the supply side: those targeting auto makers (as referred to above) and potential systems (not yet devised to our knowledge) that could target different levels of government as policymakers in supply of transport infrastructure (e.g. motorways and railways) and services (e.g. public transport).

A system of tradable permits applied to motorists

We begin by describing, in practical terms, the form that a permit system applied to motorists could take. In the case of France, private cars account for approximately three-fifth of fuel sales, the rest being consumed by light and heavy goods vehicles. We shall then evaluate this system both quantitatively and qualitatively before briefly discussing an extension of it to the freight sector.

3.1.

A tradable permit market

Obligations and permit holders

An economic incentive instrument achieves its maximum efficiency when it operates at the most decentralized level possible. In the case we are considering, this is the level of motorists as consumers of fuel and hence emitters of CO 2 so it is this group who should hold the permits and have the obligations.

A consumer who purchases motor vehicle fuel (which will necessarily be burnt) will have to transfer the corresponding quotas to the regulating authority. These quotas will then be cancelled. The quota corresponds to an authorization to emit the CO 2 equivalent of a litre of fuel2 . These quotas may be held initially by the agent or purchased from another agent who participates in the permit market.

The allocation and validity of quotas

Free allocation of permits minimizes problems of social and political acceptability as it allows a certain amount of fuel to be consumed without incurring any additional cost. This means that a minimum level of travel can be guaranteed to all users who possess no viable alternative to the car.

To do this, our starting point can be an average consumption of 1,000 litres per car per year 3 . If we impose a 10% reduction in this consumption, 900 permits should be allocated (to buy 900 litres at the normal price) per car per year 4 .

The Kyoto protocol in fact only represents a first stage towards achieving more drastic emission reduction objectives. Short-term travel behaviours are to a large degree determined by more long-term location choices -particularly residential ones. The regulating authority should therefore introduce and publicize a regular reduction in the number of permits that are allocated with a rolling horizon of about a decade.

The permits remain valid for an unlimited period, which may lead to hoarding and speculation. However, the CO 2 -equivalent value of quotas held by an agent will be reduced in the following year in accordance with the rate of the reduction in free permit allocations decided by the regulating authority.

Exchange mechanism

In order to consume more than 900 litres of fuel, a consumer must purchase additional permits on the market. On the other hand, a consumer who does not use all his/her allocated permits could sell them. The possibility of selling permits provides an additional incentive for modifying one's behaviour, particularly for persons who can do so at low cost.

However, given the huge number of potential participants, the exchange would not be bilateral, but rather centralised through a stock exchange which would yield the daily value of permit. Practically participants would buy and sell permits through intermediates like their usual bank operator or buy them at the petrol pump (see below). This means perfect information of participants about the current price of permit.

Monitoring, verification and penalties

The sale and purchase of permits will be supervised at national level by a regulatory authority. The permits which are awarded annually will be held on a chipcard which records permit debit and credit operations. This card will be compatible with the automatic teller machines (ATM) that are already installed at petrol stations. Permits can therefore be debited or purchased at the current rate when buying fuel. It will also be possible to purchase or resell permits in banks, using ATM bank distributors or over the Internet.

3 Our quantitative simulations were performed for 1997 which was the most recent year for which data on the car fleet and fuel consumption was available (the SOFRES-ADEME Parc Auto panel, cf. [START_REF] Hivert | Le parc automobile des ménages[END_REF]. Based on the mileages and unitary consumption figures which are reported by the panel (13,719 km on average, and slightly less than 7.5 l/100 km) average annual consumption is 1,022 litres. 4 Since the allocation is on annual basis, new incoming participants (e.g. individuals buying their first car) will get the same allocation as other car owners. The increase or decrease of cars will, ceteris paribus, respectively decrease or increase the individual allocation on the following year in order to comply with the overall objective.

A combined taxation and permit system

It would be socially unacceptable to apply suddenly the permits system to all motorists. The current fuel taxation system will be supplemented by the coexistence of two systems: the permits on the one hand, and the extension of taxation with a "CO 2 tax" on the other hand. These two systems will be the alternative proposed to motorists and it will be necessary to provide a financial incentive to adopt the permit system. Also, in order to reduce administrative costs, permit utilization operations will have to be validated as close as possible to the time of fuel purchase, that is to say when the motorist buys fuel at the pump. It will therefore not be possible to create an impenetrable administrative barrier between the system of taxation and the system of permits.

A possible solution is to set up a tax t (in fact the "CO 2 tax"), which would be paid both by fuel consumers who are outside the permit market and those who are taking part in it but who have used up their allocation and who are either unable or unwilling to purchase permits on the market. This tax would therefore constitute a price ceiling of permits on the market [START_REF] Baumol | The theory of environmental policy[END_REF].

This tax would have to be calculated with reference to the country's international commitments. If we take the case of France, for example, in view of the fact that the country is committed to stabilizing its emissions to the 1990 level and the increase that has occurred since then, we can make the (optimistic) hypothesis that only a 10% reduction in emissions will be required in 2008 compared to 1997.

The average price of all fuels at the pump in France in 1997 was €0.85. In order to create a strong incentive to transfer from the tax regime to the permit regime and in view of the uncertainty that affects the price elasticity, the CO 2 tax t or permit ceiling price must be based on the most pessimistic elasticity hypothesis, i.e. -0.3: this would correspond to a 33% increase in the price of fuel (inclusive of tax) i.e. €0.28 in 1997.

Taking part in the permit system could then be voluntary. Motorists would be encouraged to join the permit system as by doing so they would receive a free allocation of permits. The free allocation is linked to an act of economic consumption (possession and use of a car), which moderates the windfall effect caused by the fact that permits are free. The incentive of increasing the number of cars one owns is limited by vehicle insurance and maintenance costs, which are inescapable because periodic vehicle inspection. This windfall effect could only come into play if the cost of permits on the markets became very high: however, the price of permits is bounded by the level of tax t.

Evaluation of the proposed system in the French case

In what follows, we shall present two forms of evaluation. The first is quantitative and involves an estimation of the surpluses that result from the operation of a market of this type. The other is qualitative and involves identifying the administrative costs and a discussion of other issues associated with a system of this type. With regard to equity, surplus calculations have the advantage of showing how gains and losses are distributed on the one hand between central government and consumers in general and on the other hand between the different categories of consumers.

Evaluation of the surpluses of the different actors involved

We shall start by describing the method and hypotheses we have applied to calculate surpluses. We shall then present the results of our calculations.

Hypotheses and calculation method

Figure 1 shows a convenient approximation of the demand curve, that is to say change in demanded quantities (motor vehicle fuel, on the x-axis of this graph) as a function of the price (on the y-axis). The current exclusive of tax price (P 0 ) corresponds to that part of the price that is paid to the distributor. To this is added current taxation (VAT and excise duty) which is considered as a lump sum paid into the treasury, i.e. the price P 1 . Adding a CO 2 tax with the level of t (the price of the permit) will increase the price to P 2 .

Given the uncertainty of price response function of fuel consumers we can only hypothesize values for the price-elasticity of demand, which as stated above vary between -0.3 (short-term elasticity) and -0.7 (long-term elasticity). These values give an indication of the tax range that should be imposed a priori by the central government in order to achieve possibly the consumption reduction objective. As shown above the mechanism of permits would guarantee the quantitative objective in presence of uncertainty of price response function. Consistently with our hypotheses about priceelasticity of demand, the equilibrium price of the permit would be identical to the optimal tax in order to achieve the same consumption reduction result. This why the permit price is deliberately set at the same level of the tax in our evaluation. The transition from a price of P 1 to a price of P 2 will result in a modification of behaviours, which will in turn reduce fuel demand, from Q 1 to Q 2 . The resulting surpluses will be as follows5 :

• S 1 represents the loss in consumer surplus resulting, for example, from the reduction of trip-making or the purchase of a more fuel-efficient but more expensive car: this loss is net of the cost of the fuel that is no longer consumed (Q 1 -Q 2 ).P 1 .

• S 2 represents, in the case of taxation, the gain in central government's surplus that results from the newly paid tax on the fuel that is consumed Q 2 . S 2 is a loss for consumers. In the case of permits, central government is no longer involved and S 2 represents, for consumers, the gains that result from the sale of permits or the losses that result from the purchase of permits. • S 3 represents the loss in the surplus of central government as a result of taxes which are no longer paid on the fuel which is no longer consumed (Q 1 -Q 2 ). • S 4 represents the loss in the surplus of other agents (distributors, refiners, oil producers, etc.) because the amount of fuel (Q 1 -Q 2 ) is no longer consumed: this quantity S 4 is the same whether we consider the tax or permits: thus it does not interfere in the comparison of the two instruments.

The surplus for fuel consumers is (S 1 -S 2 ). The surplus for central government is (S 2 +S 3 ) when the tax is applied and S 3 in the case of permits. The overall surplus for society is (S 1 +S 3 +S 4 ). In these calculations, it has been assumed that variation in demand does not affect the price of fuel before tax P 0 .

In addition, as we are only comparing the tax with the permits, we take no account of gains in congestion, accidents, local pollution and noise which would result from a reduction in traffic, as these gains are similar in both cases.

Since we are evaluating different policy options to obtain a given quantitative objective of emission reduction, the overall surplus change regarding transport behaviour will be negative: this has to be compared with the infinite costs associated with climatic change which would be avoided if emissions are reduced according to the objective set by international agreements. Moreover in our exercise the overall surplus change is the same when comparing tax and permits. The differences between the two instruments lie in the distributions of surplus between categories of motorists and between motorists and the central government.

Consumers must modify their behaviours in order to reduce fuel consumption, in particular by reducing vehicle-kilometres travelled: the difficulty of this adaptation will depend on the closeness of jobs, shops and services, and supply of alternative transport modes to the car. An essential dimension therefore is the type of residential area.

Statistics concerning traffic levels and fuel consumption according to type of residential location are provided by the INRETS analysis mentioned above [START_REF] Hivert | Le parc automobile des ménages[END_REF]: this study distinguishes four types of location: the city centre, the suburbs, the periurban zone and rural areas6 .

As we do not have detailed knowledge about the elasticities for the different categories of motorists according to their residential location, we have had to hypothesize elasticity values for these four groups of motorists: it is reasonable to assume that elasticity is highest (in absolute value) for persons living in the city centre (who are the nearest to activities and who have the best public transport supply) and that this elasticity decreases as one moves towards rural zones. These values are adjusted so as to obtain the average overall elasticity level, on the basis of the percentage of vehicles originating in each category of residential location.

Using the four elasticity values we then calculate the average surpluses for each vehicle S 1 , S 2 , S 3 , S 4 , the total surplus for motorists, central government and the other actors, then the average values of these surpluses per vehicle. This calculation has been conducted for two average overall elasticity values, -0.3 and -0.7, and for the situation with taxation and the situation with permits. The detailed results of these calculations are given in the appendix.

Results

An initial comparison between the tax and the permits can be made firstly on a global basis without distinguishing between different types of residential location.

For each average elasticity value, the total surpluses and "other surpluses" (S 4 ) are identical by construction in the case of the tax and the permits. The essential difference between these two systems results from the transfers between motorists and central government.

In the case of the tax and with an elasticity of -0.3, which is the least favourable adaptation hypothesis, motorists as a group lose almost bn€7.2 and central government gains almost bn€5.1 (see Table 1 in the appendix). With an elasticity of -0.7, these values are respectively bn€3 and bn€1.2 (Table 3). As a matter of interest, the total tax collected on fuels amounted to approximately bn€30.5 in 1998, of which bn€23.6 came from excise duty. For these two elasticity values, the average additional annual tax levy per vehicle would be respectively €275 and €118 (Table 1bis andTable 3bis).

In the case of permits, these transfers are very much reduced because of the initial free permit allocation. For each of the two elasticity values (-0.3 and -0.7) motorists as a group would lose respectively €374M (Table 2) and €161M (Table 4), the annual loss per vehicle would be respectively €14 and €6 (Table 2bis andTable 4bis).

The dramatic change is experienced by central government as, with the permits, it loses more than bn€1.7 of tax revenue (Table 2 andTable 4). This is the result of the loss S 3 , due to the reduction in the amounts of fuel consumed, which are not compensated for by an additional tax which does not exist as there is redistribution between motorists as a result of permit exchanges.

Next, we can make a second comparison by observing what happens for different categories of households on the basis of residential location. On average, with the tax, the per vehicle tax levies differ by a maximum of fifty euros per year in the least favourable case (elasticity of -0.3, Table 1bis) and by about fifteen euros in the other case (Table 3bis).

The situation is of course different in the case of the permits. The volume of permit exchanges will vary according to our hypothesis concerning the elasticities for the different categories of households and the average overall elasticity.

In the least favourable adaptation situation (elasticity of -0.3), approximately 1.4 billion permits would be exchanged (Table 2ter): this figure is to be compared with fuel consumption of 26 billion litres. Households who live in city centres or the suburbs would, on average, be vendors. The monetary gain would compensate for the loss S 1 due to their lower consumption: there would be a net, but low, per vehicle gain (an average of €9 and €3 respectively over one year, see Table 2bis). Inhabitants of the periurban zone would on average be the largest purchasers and would make an average loss of €41 per vehicle over one year.

In the case of an elasticity of -0.7, about 1 billion permits would be exchanged (Table 4ter). In this case too, households located in the city centre or the suburbs would be vendors (Table 4bis). This monetary gain would just compensate for the loss that would result from the reduction in their consumption. In this case too, the biggest purchasers would be those living in the periurban areas and this group would suffer an average net loss of €16 per vehicle over the year, more than three times that of rural households (€5).

These quantitative results should, of course, only be seen as providing an order of magnitude for a possible distribution of surpluses, on the basis of the hypotheses made concerning the different elasticities according to the type of residential location. However, on the basis of these results, we can identify three factors that merit further discussion.

First, the comparison between taxation and permits in this case involves the fiscal gain in the case of the tax and the fiscal loss for the central government in the case of permits. Nevertheless, this loss would only represent approximately 5% of current fiscal revenue from fuel consumption.

Second, the tax has very little effect on the distribution of surpluses between households according to their type of residential location, as the tax levy is already very high in all cases: all motorists "lose" to the benefit of society.

Third, in the case of permits, the above tax levy disappears and residential location plays a fundamental role: the main winners are households living in the city centre or the suburbs who, on average, sell permits (they can more easily save fuel, therefore permits, by reducing their vehicle-kilometres travelled) while the households living in periurban areas are on average the largest purchasers. The orders of magnitude are of a few euros or tens of Euros of net gains or losses on average every year for each vehicle and between each category of location. Although these sums might seem small at first sight, it should be remembered that they are average results per category of motorists and may cover extremely varied adjustment behaviours.

Administrative costs

The costs of setting up and administering the system would include: • altering the software in the ATM at petrol stations so they can deal with the permit system (reading the balance, debiting); • manufacturing and distributing chipcards, or installing the microcode software on existing bank chip cards during periodic replacement; • the information campaign for this new system of transactions;

• managing the permit exchange market which could be included in the stock exchange.

In view of the fact that the transactions and verifications required for the permits will be highly integrated with the current system of credit card transactions, these costs should be moderate. Furthermore, they could be covered by a fee charged on each permit exchanged, which would be extremely low in view of the high volumes involved.

Other characteristics

This system has the advantage of simplicity, as the unit of exchange is the permit for each litre of fuel that is consumed. The amounts consumed or exchanged are therefore monitored when fuel is purchased, and all persons who purchase fuel can participate in the market (see below for the case of commercial vehicles): monitoring is therefore straightforward as it only involves fuel purchases. The fact that the tax t sets an upper bound for the price of permits and the possibility of freely exchanging permits will discourage any tendency for a black market to develop.

A similar system could also be introduced for freight and public transport vehicles. However, international competition between carriers plays an important role and regulates the transport market: this means that a permit system for commercial vehicles would have to operate at least at European Union level. Furthermore, the political difficulties involved in introducing taxes or permits in the road freight transport sector as a result of the economic fragility of many companies, should not be forgotten.

Should the permit market for the transport sector be closed or open to a national or international cross-sector permit market?

Fluctuations in the market price of permits will indicate their scarcity and the need for any adjustments. If too few permits are allocated, the price of the permits will tend to rise: however, this price is bounded by the tax t.

This kind of permits market could at the beginning operate mainly on a domestic basis: it would be viable in view of the generally short distances involved in car trips and if we ignore the impact of "tank tourism" at borders. The risk of this should be quite limited as France's neighbouring countries are also committed to reduce their emissions within the EU bubble: these countries will also have to implement either a "CO 2 tax" or a permit system. However the autonomy of each central government in fuel taxation is limited by the behaviour of its neighbouring countries as shown by the current difficulties in fuel taxation harmonisation within the EU.

If the permit market for the transport sector is closed, the price of a permit on this market could be compared with the price of a permit on another national or international market, on the basis of carbon content. It would thus be possible to assess whether the transport sector is being subjected to lower, similar or higher pressure than the others. If the pressure is insufficient, it would mean that the other sectors would have to compensate for it or that central government would have to finance the difference by buying permits on the international market. By closing the market, central government can thus decide to concentrate its efforts on one sector rather than another, for a variety of social or political reasons.

In general, if markets are closed each other, the marginal costs of reducing CO 2 emissions are likely not to be the same in different sectors. Distortions of this type will reduce the efficiency of the system. Closure of the market can therefore only be considered as a temporary measure. Ultimately, the permits market system should be open, that is to say that everyone in the country emitting GHGs in different sectors of activity would be able to exchange rights on the same market.

Acceptability and equity issues

If we consider the development of more stringent objectives of emissions reduction in the future, a fuel rationing seems unavoidable: this rationing can basically take the form of either price (tax) rationing or quantities (permits) rationing. From this point of view the issue of acceptability of rationing is an identical precondition for the two instruments and needs at least information campaign and political willpower in order to introduce any emission control measure. This is the first step which needs to be achieved 7 . This is in this context of "accepted rationing" that we can evaluate the relative acceptability of permits.

The free allocation of emission rights creates income which is distributed between the consumers of fuel. In addition, these consumers are strongly encouraged to reduce their consumption as they can make a real and tangible profit from selling their unused permits. 7 Recent examples show that opinion can rapidly and significantly change and accept "unpleasant" policies. This is the case of congestion charging in London supported by a strong political willingness of the candidate and then Mayor of London Ken Livingston. This is also the case with the stronger enforcement of speed limits decided in September 2002 in France by the government: this policy overcome decades of laxity and increase of road fatalities.

If all vehicles are allocated the same number of permits problems of equity can arise as a result of specific constraints of use: families with children, disabled persons, persons living in rural areas, etc. There is no reason why the free allocation of permits should not be based on socioeconomic characteristics. It would also be possible for permits to be allocated to each individual, irrespective of their age and whether they own a car.

If we consider again the French case study, this system penalizes high income households more than others: the data from 1997 [START_REF] Hivert | Le parc automobile des ménages[END_REF] show that the average per kilometre mileage for each vehicle increases fairly steadily with income bracket, from slightly more than 12,000 km for the lowest income brackets (less than 11.4 thousand euros per year) to almost 16,000 km for the highest income brackets (more than 61 thousand euros per year).

Lastly, the initial free allocation avoids imposing an excessive burden on consumers, particularly the least well off. The average annual consumption of cars varies from slightly more than 900 litres (for the lowest incomes) to 1300 or 1400 litres (for the highest incomes), while the proportion of mileage that is covered on home-towork trips varies between 24% (for the lowest incomes) and 30 or even 39% for the highest income groups. These figures show that "necessary" travel would generally not be affected. However, this average data should not obscure a possible existence of situations of fragility, for example the "rural poor" who have no alternative but the car; such situations would require ad hoc compensation.

Conclusion

In this paper we have shown how decentralized transferable permit systems for the transport sector are of interest with regard to reducing greenhouse gas emissions, in spite of anticipated transaction costs. Next, a system of tradable permits for motorists has been described, and its technical and economic feasibility investigated: the marginal costs of depollution vary sufficiently according to motorists' residential locations for us to envisage permit exchanges. Last, we have outlined an evaluation of the socioeconomic consequences of this market operation and the surpluses that would result from it, with plausible elasticities derived from empirical studies.

These simulations have shown that with a system of permits that can be transferred between motorists, central government would only lose 5% of its fiscal revenue from fuel taxes. The loss in surplus for motorists would be of the order of €10 per vehicle on average in the case of permits as opposed to between €100 to €275 on average in the case of a CO 2 emission tax: this is obviously a factor that supports the acceptability of a permit system. The number of exchanges would be large, of the order of one billion permits per year (with a cost of between €0.12 and €0.28 per permit). Residents of city centres and suburbs would, on average, tend to sell permits while those in periurban areas or in rural areas would tend to purchase them.

One of the main objections to the application of a system of tradable permits to the transport sector is the large number of actors involved. The resulting transaction costs would be too high for the system to be effective. The system that we have described in this paper overcomes many of these constraints. Its implementation would nevertheless be complex and administratively more costly than a simple increase in fuel taxation.

However, this system does provide strong incentives for reducing consumption because of the concrete, tangible, benefits perceived by those who reduce their emissions below their initial allocation. The free allocation of permits furthermore provides a means of overcoming problems of accessibility and equity which would be posed by the addition of a new tax on an already heavily taxed product such as fuel.

Another advantage of this system is that a permit based on the carbon content of fuel can be directly linked with the world market for permits in order to avoid inefficient price distortions between these markets. Nevertheless, central government could maintain complete control over the domestic market and would thus be able to protect it from fluctuations on the world market.

Figure 1 :

 1 Figure 1: The effects of taxes on the demanded quantities of fuel and the distribution of surpluses

Table 1 Table 1bis change in surplus with permit

 1

				average		variation in
				total	litres /	average	vehicles
		estimated	average vkt	consum.	100km	consum.	(million)	% of
	Location	elasticity	(1)	(2)	(3)	(4)	(5)	vehicles
	city centre	-0.55	12 918	980	7.58	-179	7.2	27
	suburbs	-0.40	12 869	977	7.59	-130	7.3	28
	periurban	-0.10	14 809	1 085	7.33	-36	10.7	41
	rural	-0.05	14 035	988	7.04	-16	1.0	4
	average	-0.3	13 719	1 022	7.46	-101	26.2	100
						(1) per vehicle per year. Based on survey findings
	Average price in 1997 (€)		0.85		(2) in litres / vehicle per year. Based on survey findings
	of which existing taxes		0.65		(3) ratio between (1) and (2)
	Tax or permit price		0.28		(4) in litres / vehicle. Application of price elasticity
	Initial price + tax		1.13		(5) based on survey findings
	Permit allocation (litres)		921
	change in surplus with fuel tax
	average per vehicle
								central				central
		S1	S2	S3	S4		users	gov.	others	total	user	gov.	others	total
	Location	(€)	(€)	(€)	(€)		(M€)	(M€)	(M€)	(M€)	(€)	(€)	(€)	(€)
	city centre	-25	226	-117	-36		-1 806	788	-257	-1 275	-252	110	-36	-178
	suburbs	-18	240	-85	-26		-1 892	1 137	-191	-946	-258	155	-26	-129
	periurban	-5	297	-23	-7		-3 229	2 923	-77	-383	-302	273	-7	-36
	rural	-2	275	-11	-3		-272	259	-3	-16	-277	264	-3	-16
						overall:	-7 198	5 107	-528	-2 620	-275	195	-20	-100
	average per vehicle
								central				central				permit
		S1	S2	S3	S4		users	gov.	others	total	user	gov.	others	total		exchanges
	Location	(€)	(€)	(€)	(€)		(M€)	(M€)	(M€)	(M€)	(€)	(€)	(€)	(€)	Location	(millions)
	city centre	-25	34	-117	-36		64	-836	-257	-1 029	9	-117	-36	-144 city centre	870
	suburbs	-18	21	-85	-26		20	-620	-191	-791	3	-85	-26	-108 suburbs	546
	periurban	-5	-36	-23	-7		-441	-251	-77	-770	-41	-23	-7	-72 periurban	-1 367
	rural	-2	-14	-11	-3		-16	-10	-3	-30	-16	-11	-3	-30	rural	-49
					overall:		-374	-1 718	-528	-2 620	-14	-66	-20	-100		0

Table 2 Table 2bis Table 2ter entire fleet average per vehicle entire fleet average per vehicle

 22bis

				average		variation in
				total	litres /	average	vehicles
		estimated	average vkt	consum.	100km	consum.	(million)	% of
	Location	elasticity	(1)	(2)	(3)	(4)	(5)	vehicles
	city centre	-1.00	12 918	980	7.58	-139	7.2	27
	suburbs	-0.85	12 869	977	7.59	-118	7.3	28
	periurban	-0.45	14 809	1 085	7.33	-70	10.7	41
	rural	-0.40	14 035	988	7.04	-56	1.0	4
	average	-0.7	13 719	1 022	7.46	-102	26.2	100
						(1) per vehicle per year. Based on survey findings
	Average price in 1997 (€)		0.85		(2) in litres / vehicle per year. Based on survey findings
	of which existing taxes		0.65		(3) ratio between (1) and (2)
	Tax or permit price		0.12		(4) in litres / vehicle. Application of price elasticity
	Initial price + tax		0.97		(5) based on survey findings
	Permit allocation (litres)		921
	change in surplus with fuel tax
	average per vehicle
								central				central
		S1	S2	S3	S4		users	gov.	others	total	user	gov.	others	total
	Location	(€)	(€)	(€)	(€)		(M€)	(M€)	(M€)	(M€)	(€)	(€)	(€)	(€)
	city centre	-8	102	-91	-28		-789	79	-200	-910	-110	11	-28	-127
	suburbs	-7	104	-77	-24		-814	198	-173	-789	-111	27	-24	-108
	periurban	-4	123	-45	-14		-1 359	831	-149	-677	-127	78	-14	-63
	rural	-3	113	-37	-11		-114	75	-11	-50	-116	76	-11	-51
						overall:	-3 076	1 183	-533	-2 426	-118	45	-20	-93

Table 3 Table 3bis change in surplus with permit

 3

	average per vehicle
							central				central				permit
		S1	S2	S3	S4	users	gov.	others	total	user	gov.	others	total		exchanges
	Location	(€)	(€)	(€)	(€)	(M€)	(M€)	(M€)	(M€)	(€)	(€)	(€)	(€)	Location	(millions)
	city centre	-8	10	-91	-28	9	-650	-200	-840	1	-91	-28	-117 city centre	577
	suburbs	-7	7	-77	-24	2	-563	-173	-734	0	-77	-24	-100 suburbs	453
	periurban	-4	-12	-45	-14	-168	-483	-149	-800	-16	-45	-14	-75 periurban	-1 019
	rural	-3	-1	-37	-11	-5	-36	-11	-52	-5	-37	-11	-53	rural	-11
					overall:	-161	-1 732	-533	-2 426	-6	-66	-20	-93		0

Table 4 Table 4bis Table 4ter entire fleet average per vehicle entire fleet average per vehicle

 44bis

the price elasticity of fuel demand is the sensitivity of fuel demand to price: an elasticity of -0.3 means that an increase in price of 10% yields a decrease in demand of 3%.

Strictly speaking, this value should vary according to the type of fuel: diesel fuel contains more carbon than petrol, gasoline with ETBE can have different emissions than gasoline without ETBE. A conversion factor would apply for each kind of fuel. For the purpose of simplicity of exposition and evaluation in this paper we have assumed that one permit unit corresponds to one litre of any fuel.

In what follows, the surpluses are considered to be positive for the agents who benefit from a gain and negative for the agents who suffer a loss.

This coding was developed by INRETS, cf.[START_REF] Madre | Comment décrire l'étalement urbain à partir des nomenclatures de l'INSEE ? Note interne INRETS[END_REF]

This paper is based on a research conducted with the support of the CNRS (Centre National de la Recherche Scientifique) and funded by the French Ministry of the Environment. We would also like to thank our colleague Dominique Bouf for his helpful comments on an earlier version of this paper. However views expressed here are solely the authors' ones.


Mohieddine Missaoui
email: missaoui@isima.fr

Cécile Militon

David Hill

Christophe Gouinaud

Pierre Peyret

PRT: Parallel program for a full backtranslation of oligopeptides

Keywords: Oligopeptide, Probe design, Full back translation, Parallel computing

DNA hybridization methods have become the most widely used tools in molecular biology to identify organisms and evaluate gene expression levels. PCR (Polymerase Chain Reaction)-based methods, fluorescent in situ hybridization (FISH) and the recent development of DNA microarrays as a high throughput technology need efficient primers or probes design. Evaluation of the metabolic capacities of complex microbial communities found in terrestrial or aquatic environments requires new probe design algorithms that reflect the genetic diversity. As only a small part of the microbial diversity is known, gene sequences deposited in international databases do not reflect the entire diversity. In this context we propose to use oligopeptide sequences for the design of complete set of DNA probes that are able to target the entire genetic diversity of genes encoding enzymes. Due to the degenerated genetic code backtranslation must be managed efficiently. To our knowledge no software has been developed to propose a full backtranslation. This complexity is tractable since we only need to focus on short oligopeptides for DNA probe design. We propose new algorithms that perform a high performance oligopeptide backtranslation into all potential nucleic sequences. We use different efficient techniques such as memory mapping to perform such a computing. We also propose a MPI parallel computing that reduces the whole execution time using data load balancing and network file stream distribution on a cluster architecture.

I. INTRODUCTION

The overwhelming majority of life on our planet is microbial, both in terms of phylogenetic diversity and sheer number of organisms. Virtually every conceivable environmental niche harbours microorganisms capable of growing there. Traditional microbiological methods of cultivation recover less than 1% of the total bacterial species, and the cultured portion of bacteria is not representative of the total phylogenetic diversity. Considering the extent of functional diversity described for microbes and the numerous applications of their secondary metabolites, the biotechnological potential hidden among the 99% of the bacteria that are uncultured is immense. Deciphering the microbial metabolic pathway capacities in complex environments (soils, lakes, oceans…) is essential for the protection of the environment. However, conventional biochemical and molecular methods (PCR-based technologies) for assessing microbial community structure and activities are labour-intensive. Microarrays are a powerful tool for the parallel, high throughput detection and quantification of many nucleic acid molecules [START_REF] Bodrossy | Oligonucleotide microarrays in microbial diagnostics[END_REF]. Oligonucleotide microarrays are the most widely developed tools for microbial diagnostics. However, probe design is not a trivial task and needs particular attention [START_REF] Rimour | GoArrays: highly dynamic and efficient microarray probe design[END_REF]. Functional gene arrays (FGAs) contain probes corresponding to genes encoding key enzymes involved in various ecological and environmental processes such as carbon fixation, nitrification, denitrification, sulphate reduction, methane oxidation, and contaminant degradation. Both PCR-amplified DNA fragments and oligonucleotides derived from functional genes can be used to manufacture FGAs. In each situation we need to know the gene sequences for the probe design. As a large part of microbial diversity is unknown we can only use sequences from genes deposited in international databases. To develop an explorative aspect for functional microarrays we propose to design probes derived from the protein sequences. In this context we are able to determine the probes sets that characterize an enzyme or a metabolic pathway of interest. We have developed full backtranslation algorithms for oligopeptides able to provide interesting DNAs sequences for probe design in the context of functional microarrays.

II. MATERIALS AND METHODS

A. Related Works

Parallel computing is often the best solution to optimize bioinformatics algorithms which are time and memory consuming [START_REF] Suyama | PAL2NAL: robust conversion of protein sequence alignments into the corresponding codon alignments[END_REF]. Computer architectures such as computing clusters and grids are now appropriate for many bioinformatics applications [START_REF] Melab | Grid computing for parallel bio inspired algorithms[END_REF]. The backtranslation problem appeared after the protein synthesis mechanism discovery [START_REF] Nirenberg | Historical review: Deciphering the genetic code--a personal account[END_REF] followed by the entire genetic code decoding in 1961 by the Nobel Prize laureate M. Nirenberg. Therefore, Bioinformatics was incidental to biology advancement and contributed to solving difficult problems such as local and global sequences alignment. Backtranslation is most often required in larger applications using protein to DNA or RNA passing. Studying phylogeny uses genetic code to perform a phylogenetic tree construction based on sequence homology detection. Information detained by proteins is useful when constructing optimal multiple DNA alignments for phylogenetic analysis [START_REF] Wernersson | RevTrans: multiple alignment of coding DNA from aligned amino acid sequences[END_REF]. In this case, backtranslation is simply a replacement of amino acid by the existing codon in the initial corresponding nucleic sequence. Thus, passing from protein to DNA can preserve this phylogenetic information.

Nevertheless, genomic and transcriptomic databases are used as a source of sequences existing in protein alignment, so it is possible to find CDS (CoDing Sequences) [START_REF] Moretti | PROTOGENE: turning amino acid alignments into bona fide CDS nucleotide alignments[END_REF] by launching a BLAST [START_REF] Altschul | Basic local alignment search tool[END_REF] program and then construct the alignment using the ClustalW [START_REF] Chenna | Multiple sequence alignment with the Clustal series of programs[END_REF] program. Similar tools that use backtranslation to perform an alignment are available [START_REF] Bininda-Emonds | transAlign: using amino acids to facilitate the multiple alignment of protein-coding DNA sequences[END_REF] [START_REF] Suyama | PAL2NAL: robust conversion of protein sequence alignments into the corresponding codon alignments[END_REF].

Moreover, using backtranslation can be made for direct derived nucleic sequences search from a protein sequence. Most of them are based on IUB/IUPAC degenerate nucleotide base codes [START_REF] Pesole | A backtranslation method based on codon usage strategy[END_REF], which assume the use of a consensus sequence to represent all possible sequences corresponding to the initial protein. Figure 1 shows consensus triplet codons of all amino acids using IUB degenerate nucleotide base codes. With this approach, one protein is backtranslated to a unique IUB codon that represents all possibilities in only one nucleotide triplet. Software that uses IUB codes to reverse translate a protein only uses a replacement of their amino acids by corresponding codons. Consequently, to obtain a nucleic sequence from input peptide, all we have to do is to combine the known codons in the appropriate order.

A C D E F G H I K L M N P Q R S T V W Y *

Reverse translation with degenerate code GCNTGYGAYGARTTYGGNCAYATHAARMTNATGAAYCCNCARMGNWSNACNGTNTGGTAYTAR Fig. 1. Consensus nucleic sequence of a backtranslated peptide using IUB degenerate nucleotide base codes. This example shows all possible reverse translations (20 amino acids plus "STOP" codons given by '*').

Reverse translation can be also used to calculate probable DNA codon usage for an organism [START_REF] Nash | A computer program to calculate and design oligonucleotide primers from amino acid sequences[END_REF]. It can use genetic algorithm [START_REF] Moreira | TIP: protein backtranslation aided by genetic algorithms[END_REF] to determine the most probable codon at a given position by launching a data mining algorithm on a selected databank. In addition, some software uses neural networks data mining to similarly perform the same task [START_REF] White | Using a neural network to backtranslate amino acid sequences[END_REF]. An additional method is based on hierarchical clustering data mining to do this backtranslation [START_REF] Ma | Cluster analysis of the codon use frequency of MHC genes from different species[END_REF]. We note that several methods use particularly data mining algorithms or distance matrix to find the most adapted reverse translation of a peptide [START_REF] Stothard | The sequence manipulation suite: JavaScript programs for analyzing and formatting protein and DNA sequences[END_REF]. The software returns the most probable codon for a given species as shown in Figure 2. Similar tools which use the most probable codon or user-selected codons to perform such a reverse translation are available by web interface [START_REF] White | Using a neural network to backtranslate amino acid sequences[END_REF][START_REF]WebLab: backtranseq[END_REF][START_REF]CLC Protein Workbench[END_REF]. From the previous works, and to the best of our knowledge no tool is available to automatically perform a full backtranslation providing all possible non degenerate DNA sequences corresponding to an input oligopeptide. In the next section we present high performance parallel algorithms able to use cluster and grid resources to take up this challenge. This work is limited to oligopeptide since it is practically impossible to produce all the DNA sequences corresponding to a protein, or even to a long peptide. The main reason is simply the unfeasibility of storing the results because of space and time constraints.

B. Why do we need a complete backtranslation?

Our method aims to show all potential DNA sequences that could spark a given oligopeptide sequence for the development of functional microarrays used in microbial ecology. Our approach supposes that the maximum length of the DNA generated sequences does not exceed 24 bases because the target sequences are probes which will serve in biochip design such as what we proposed in [START_REF] Rimour | GoArrays: highly dynamic and efficient microarray probe design[END_REF]. Thus, the given peptides used on backtranslation process will be about 6 to 8 amino acids. Furthermore, backtranslation is still ambiguous due to its memory-time consuming nature mainly caused by the genetic code degeneracy. Two approaches are presented here; both use the genetic code degeneracy to construct the algorithm. The main difference between the two approaches relies on data manipulation.

C. The Mathematical Model

We propose a new algorithmic approach to construct backtranslated DNA sequences from a protein sequence. Let Γ = {A, C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y,*} and Σ = {A, C, G, T} be the alphabets for amino acids and nucleotides, respectively. Let ϕ : Σ 3 → Γ be the translation of a DNA sequence according to the genetic code. We denote card(ϕ -1 (X)) the number of triplet codons that code for the amino acid 'X'. It is called the degeneracy of the amino acid 'X'. We named the algorithm PRT for oligoPeptide Reverse Translation. This algorithm can be assimilated to a function:

PRT n (p): Γ n → δ n (p) × ( ) Σ 3 × n (1)
Given an oligopeptide 'p' of length 'n', the function will return PRT n ( ) p DNA sequences;

PRT n ( ) p is the total degeneracy of the input sequence 'p'; it depends both on the sequence and on its length. Therefore, for an oligopeptide X 1 X 2 X 3 ...X n , we have:

δ n (p) = ∏ i = 1 n card     ϕ -1 ( ) x i (2)
Our algorithm uses the PRT n procedure (see equation 1) to compute non degenerated DNA sequences.

D. Algorithm principle

Let p = X 1 X 2 X 3 ...X n be a peptide of 'n' amino acids. Let X i ; 1 < i < n be an amino acid of the peptide 'p' in position 'i' (see figure 3). We denote d(i) the calculated degeneracy from the initial position to position 'i'.

d( ) i = ∏ k = 1 i card     ϕ -1 ( ) x k (3)
We denote r(i) the remaining degeneracy in step 'i':

r ( ) i = δ n ( ) p d ( ) i (4)
We describe in details our algorithm as follows:

(1) For the i th amino acid, append current codons according to degeneracy variable (see below) in the appropriate order (see the following algorithm)

(2) Save the result in a structure

end while

This algorithm can be transposed using several techniques. We implemented the different techniques using the C language capabilities. In this paper we show the most efficient strategies we obtained. Additionally, our approach depends neither on the peptide length nor on the sequence composition. The latter are computed by the algorithm according to the codons table.

E. Computer systems

The computer used for this study is a bi-processor equipped with an Intel (R) Xeon TM at 2.4

Ghz with 2 Gb of RAM. For sequential tests, we used a single processor. We developed the algorithm using the C language with a GNU C compiler (version 3.4.1).

F. Backtranslation strategies

Two strategies based on the PRT n algorithm are presented here. A comparison between the two implementations will give us decisive elements in order to retain the best solution for a specific problem.

1) Dynamic memory allocation

The first strategy adopted to develop the PRT algorithm was to use a large array preallocated in dynamic memory. We used a pointer data structure to store output data consisting of generated backtranslated DNA sequences from the input peptide. Furthermore, the algorithm uses this data structure and the codon table structure. A single line of code is required to store data in the structure. The storage of sequences follows the data structure presented in figure 4 exactly.

2) File memory mapping

The second method used to perform backtranslation is based on file memory mapping.

We launch the algorithm to write the output nucleic sequences in a memory file managed like a pointer. In our C code, we use appropriate structures such as start and end mapped file pointers. First of all, we create a file formatted according to the output. Then, each codon is placed by the algorithm in the appropriate position in the file. The position is computed for each amino acid. Using file memory mapping management strategy is particularly interesting because in opposition to dynamic memory allocation we save sequences directly in the output file and we don't introduce an intermediate data-structure. Though we rely on a file, we are limited by the system RAM as with the dynamic allocation method. Copying results (codons) is done nucleotide by nucleotide for each codon. This slows down the execution time, but it remains more efficient than the dynamic memory allocation strategy. We copy codons to the output oligos file using a file descriptor pointer that moves by finding the appropriate position of each codon. The output file is used like a table structure so we can easily manipulate its indexes.

The method can be used with memory mapping only if we assume that output oligos are stored in a file because we made preliminary actions and dedicated variables initialization to run this algorithm : we should declare a size, a file status and a file descriptor to be able to use memory mapping capabilities. Our algorithm uses different pointers to move along the mapped file.

III. RESULTS

A. Sequential Performance comparison

Execution time decreases when we use the memory mapping approach because we write the nucleic sequences directly in the output file, as shown in figure 5. We launched the tests on an isolated computer to assert that the system overhead and load was the same.

Fig. 5. Performance of both strategies used for backtranslation (the length of peptide is minimal for each tested degeneracy). For example, if we take degeneracy 20155392 it corresponds to RRRRRRRRRK oligopeptide which is the shortest peptide for this degeneracy.

In figure 5, the difference in execution time between the two strategies is due to the memory allocation performed by the dynamic approach. When the dynamic structure is full we print out the results in an output file of oligonucleotides. To be able to compare the two strategies we must have an unlimited memory system; which is not reasonable. Table 1 shows execution time of the two backtranslation strategies. We reported the whole execution time returned by Linux 'time' function. As expected, we observe that if the peptide degeneracy increases, the performance exponentially decreases. In fact, our algorithm has to handle an exponential complexity, and even if the problem is tractable for oligopeptides, it can require a significant amount of disk space. . This disk space (RDS : Required Disk Space) can easily be predicted for a given oligopeptide. It depends on (p) and is given by the following equation:

RDS = [ ] δ n ( ) p ×( ) n ×3 + 1 Bytes (5)
For an oligopeptide having a degeneracy around 10.10 6 , a single computer (see the Computer System section) requires less than 300 Mb of disk space and less than 30 seconds of execution time in the case of memory mapping strategy. In the study described by Tamura et al., (1991), the degenerate code used to a find consensus nucleic sequence backtranslated from a peptide does not require more than 3 times the size of the input peptide. In our new approach, we should save all obtained sequences for only one oligopeptide. In practice, we need to work with several thousand of oligopeptides. However, there is no need to keep the resulting DNA sequences for all oligopeptides, they can be processed to design DNA probes one by one and peptide by peptide. However, in order to increase the throughput, parallel computing is well-adapted to reduce the complexity of this algorithm. In fact, the backtranslation step is time-consuming because we try to backtranslate a large number of oligopeptides knowing that the whole execution time increases when we work on long oligopeptides. In the next section, we present Parallelization methods for our two algorithm variants using the MPI library. The algorithms developed were run on a local cluster architecture.

B. Parallel implementation

Even id a sequential approach is satisfactory, a parallelization process is interesting to to optimise the performances of our algorithms. A local cluster architecture is perfectly adapted to this kind of application. In the following section, we describe adaptations of the algorithms which optimize the resources of a cluster computing environment. This approach achieve high throughput non redundant protein to DNA backtranslation, it reduces the whole execution time and the results are dispatched on several disks to avoid disk space overloading.

C. The computing cluster architecture

A computing cluster is an homogeneous systolic architecture, which uses the power of interconnected machines to perform time consuming tasks. We have used the following cluster architecture: a system of 15 PCs (one master with an Intel Xeon, To have an efficient parallelization for the two strategies -dynamic memory allocation and file memory mapping -we opted for a load balancing approach and a distribution of output files on all used nodes. In fact, each process (assigned to a node) computes a part of the whole result for a given peptide and locally save fragment results. Fragments are equally distributed on the cluster in order to have maximal performance and storage balancing on each node. MPI was used to dispatch data on all nodes and to subdivide computing for each process. Table 2 shows the execution time of the two parallel strategies Memory allocation specifically uses system memory but the memory mapping strategy only uses CPUs and IOs. Our algorithms construct for each node their own fragment structures by the two approaches and then perform locally the appropriate computation for each fragment oligos. To have such results, we split output data into 14 structures because we have 14 nodes; each structure contains the ordered oligos. For example, the oligo numbered 'n' is stored on node number 'x' and the oligo numbered 'n+1' is stored on node number 'x+1'; if x = 14 then oligo number n+1 is stored on node number 1 and so on until the last oligo. Moreover, each amino acid is processed as in the sequential algorithms. As mentioned in the previous section, the execution time for the sequential algorithms increases exponentially when input peptide degeneracy exceeds 3.10 6 oligos; but, with parallel approaches, we obtain the histograms shown in figure 6.

Parallel implementation shows a decrease in the whole execution time compared to sequential algorithms for the two approaches. We can even see a linear increase for the dynamic memory allocation up to degeneracy of 6 10 . Dynamic memory allocation is more advantageous for small degeneracy peptides (< 6 11 ). Memory mapping execution time increases faster than dynamic memory allocation because the CPUs are used every time for computing codons and file pointer position. The algorithm using memory allocation has been parallelized by sharing memory and output data between Cluster nodes.

1) Performance Balance

Using a cluster framework to compute oligos generated from a peptide backtranslation by parallel programming with MPI shows an improvement of the whole performance. In fact, such a distributed system offers multiple resources to compute a large number of oligos efficiently. Figure 7 shows that the time gain is enhanced when degeneracy increases if we use a parallel backtranslation on a computer cluster. We can observe that the file memory mapping approach is more efficient in the case of the sequential algorithms but, in the parallel version, we can see a better behaviour of parallel dynamic allocation. Performance declines when we try to find long oligos with high degeneracy (50 bases and more). We surpass system capacities: CPU, memory, and disk space when we work with oligopeptides of 30 amino acids and a degeneracy greater than 6 13 . In addition, Figure 8 evidences the relevance of parallel codes for such work. It shows that when we use a cluster architecture algorithm to backtranslate a 6 9 degeneracy oligopeptide, performance increases with the two previously mentioned strategies. In fact, the whole execution time decreases when algorithms use more and more nodes. The complexity remains exponential, but it can be significantly decreased by the number of computing nodes. When we work on short oligopeptides we cannot distinguish the difference between parallel and sequential algorithms. Indeed, the oligpeptide length has an incidence on the whole execution time, as for sequential programs(when the length increases, the performance logically decreases).

IV. CONCLUSION

This paper introduces a novel approach giving a full backtranslation of oligopeptides and brings to light the utility of such a method in enzyme specific oligos design. This approach is able to produce all possible non degenerate DNA sequences corresponding to an input oligopeptide of reasonable degeneracy. This problem presents an exponential complexity and we have presented a new algorithm implemented with the C programming language with two different strategies minimising the execution time. In addition, we propose a parallel version of the two strategies developed using MPI in a computing cluster environment. The parallelization helps in dividing the algorithm complexity which remains however exponential. Performance tests indicate that the parallelization has clear advantages because it allows the fragmentation of the output oligos file knowing that a full backtranslation need significant disk space.

Fig. 2

 2 Fig. 2 Nucleic acid sequence determination by backtranslation based on the preferential genetic code usage in E. coli species. (See http://cgpdb.ucdavis.edu/database/sms/javascript/index.html for more details).

  Input: peptide of n lengthOutput: file of generated oligos while i <= n do repeat (for each codon of x i ) d (i)/card (ϕ -1 (x i )) times repeat append (codon) r (i) times;

Fig. 3 .

 3 Fig. 3. An example to highlight the algorithm operation for backtranslation

Figure 4 Fig. 4 .

 44 Fig. 4. Dynamic Allocation main storage data structure. This C data structure is used to store all generated probes

Fig. 6 .

 6 Fig. 6. Performance of parallel algorithms. The two parallel approaches compared.

Fig. 7 .

 7 Fig. 7. Parallel vs. sequential backtranslation programs. The parallel versions of our algorithm shows a liner like curve for degeneracy smaller than 4.107.

Fig. 8 .

 8 Fig.8. Cluster computing speedup for the two studied strategies. The speedup is given by the quotient between the sequential execution time and the parallel one.

TABLE 1 .

 1 DATA OF PERFORMANCE COMPARISON FOR THE TWO STRATEGIES USED FOR BACKTRANSLATION. IT BELONGS TO FIGURE 5.

TABLE 2 .

 2 PERFORMANCE DATA COMPARISON BETWEEN THE TWO PARALLEL ALGORITHMS.

ACKNOWLEDGEMENTS

This work was financially supported by the regional council of Auvergne (PREVOIR and INSTRUIRE projects) and by a grant from the ACI Non Pollution-Dépollution, « Oxygen » project. M. Missaoui was supported by a grant from the regional council of Auvergne and C.

Militon by a grant from "Ministère de l'éducation, de la recherche et de la technologie". The authors thank Pr. Philip Hoggan for his helpful advices.


Séverine Bernardie

Nicolas Desramaut

Gaëtan Russo

Gilles Grandjean

Gilles Grandjean Prediction

Prediction of changes in landslide movements induced by rainfalls: from the use of a black box model to a 1D mechanical model

Prediction of changes in landslide movements induced by rainfalls: from the use of a black box model to a 1D mechanical model

S. Bernardie (1), N. Desramaut(2), G. Russo(2), G. Grandjean(2)

(1) BRGM, Orléans, France (s.bernardie@brgm.fr),

(2) BRGM, Orléans, France

Predicting landslide surface displacements is a challenge for scientists, as it may help save human lives and protect individual housing or transport, energetic facilities. One of the main challenges in active landslide monitoring concerns the prediction of slope's movements in the near future. This study focuses on an innovative methodology to predict landslide surface accelerations, based on a black box tool coupled to a 1D mechanical model. These models are able to predict the evolution of the daily displacements according to the variations of precipitation. More specifically, the impulse response model allows predicting the changes in the landslide movements by computing the transfer function between the input signal (precipitation in this case) and the output signal (the displacements). The second model is based on a simple 1D mechanical assumption, with considering a viscoplastic behavior of the landslide's material, and with taking into account the evolution of the pore water pressure in time.

These methods have been applied to the Super-Sauze landslide, located in the Southern French Alps, mountainous region. This site is controlled by complex hydrologic processes leading to active movements within black marls, with velocities ranging between 0.002 and 0.4 m per day. After preliminary tests, results show that the snowmelt has to be taken into account in the models, since the phenomena of freezing /thawing has an influence on the water refills, leading to movement changes. Different approaches to integrate rainfall and/or snow-melting inputs are compared and their complementarity is demonstrated. Finally, a validated methodology for predicting movement changes within landslide based on criteria of comparison between the observed and calculated velocities can be proposed. The results suggest that the impulse response model reproduces the observed data with very good accuracy, whereas the mechanical model seems to be more adapted to predict the movements within 10 days. Moreover, the RMSE criterion permits to highlight the occurrence of the flow, with considering all models, 11 days before the flow itself.


Modelling the behaviour of a large landslide at Reunion Island (Grand Ilet)

S. Bernardie (1), B. Aunay (2)

(1) BRGM, Orléans, France (s.bernardie@brgm.fr), (2) BRGM, Regional Geologic Service of Languedoc-Roussillon-Montpellier, France One of the main challenges in active landslide monitoring concerns the prediction of slope's movements in the near future. Understanding the initiation mechanisms of the mass movement is a key towards predicting its evolution. This study concerns a large landslide in the Reunion Island (Grand Ilet), where the extreme climatic conditions (cyclonic activity) produce large deformations within the active landslide, resulting in displacements large as 3 cm per 12 hours. The surficial moving layers are constituted two layers: the first one is characterised by heterogeneous volcanic terrains; the upper layer is constituted of breccia materials resulting from ancient debris avalanche. The thickness of the surficial moving layers is high, ranging from 80m to 200m. The objective of the study is to understand the mechanisms leading to the evolution of the mass movements. For that, characterization of the site, monitoring of the movement, and modelling the hydromechanical processes are necessary. Moreover, different hypotheses of the initiation of the landslide have to be tested. In particular, the evolution of the water level correlated to the precipitations, as well as the erosion of the toe of the landslide, are analyzed. Characterization of the landslide is performed through different in situ measurements, such as electrical tomography. It permits to assess both the geometrical and geomechanical characteristics of the unstable mass. In situ mechanical tests have also been realized to obtain geomechanical parameters useful for the hydromechanical model. All the measured geometry and parameters of layers are then included in a 2D finite element model. The computations are performed using a finite element code with an infinitesimal strain and twophase formulation assumptions. Preliminary geomechanical simulations are realized, permitting to highlight the hydraulic conditions changes on the mechanical behavior of the landslide. The computed displacements are then compared to the recorded data. The results are analyzed and discussed.