Simon Gorecki

Youssef Bouanan

Gregory Zacharewicz

Judicael Ribault

Nicolas Perry
email: perry.nicolas@ensam.eu

Integrating HLA-Based Distributed Simulation for Management Science and BPMN

Keywords: Modeling and Simulation, Distributed Simulation, High Level Architecture, Business Process Model and Notation, Interoperability

Modeling and Simulation are becoming more and more complex, making their design very challenging. Modeling and Simulation of complex systems requires simultaneous consideration of several points of view and the study of these systems needs skills belonging to different scientific fields. In Distributed Simulation domain, IEEE 1516-2010 -High Level Architecture (HLA) is one of the most used standard. However, it does not provide any official graphical language for defining distributed simulation behaviors. Business Process Model and Notation standard could be an interesting solution for defining HLA execution scenario. This paper present application experiment applied to solar power plant. Our proposition consists in restrict the HLA execution process in order to use one federate as Master, controlling the others as Slaves. This allows us to generate a component responsible for the simulation execution process with parsing a Business Process Model and Notation diagram. In this paper, we present an application of this concept.

INTRODUCTION

The Modeling and Simulation (M&S) concept is now a required step in any design of complex systems. It allows to early represent its behavior and interaction. The modeling phase describes a process and allows the development of an executable simulation which virtually designs our subject and anticipates its study. As technologies are growing, the systems complexity increases, and makes the system more difficult to simulate. Here comes the role of Distributed Simulation (DS): one simulation is divided into multiple sub simulations (or models) from a complex system. Each autonomous simulation is executed on a different computer possibly geographically distributed from others. From a general point of view, this solution divides into modular simpler sub problems from complex problems, but also rises interoperability issues.

M&S of complex systems requires the simultaneous consideration of several points of view. The System behavior has to be considered at different levels and scales. In addition, the study of these systems involves skills from different scientific, business and technical fields. The challenge is then to reconcile these heterogeneous domains, and to integrate each domain models and tools (or subsystems) within frameworks of the M&S process.

In our case, we will use various M&S technologies in a semiacademic, semi-professional context: a French company has launched an innovative project to set up a solar power plant. This project deals with different domains including risks management. Most of these research works have created specific domain simulators. Each of these autonomous simulations can represent a fragment of the global project. One of the last phases of this project consists in coupling all these simulations to obtain a global simulation of the problem to treat. However, all of these simulations use different technologies and manipulate heterogeneous data. It complicates the coupling. As a response to these difficulties, we propose to use the High-Level Architecture (HLA) standard. Moreover, there is a special need of reusability in our context. Indeed, the company needs to reuse and run different components without any HLA knowledge. It is the issue we try to solve in this paper.

HLA is one of the most used standard specification software architecture for Distributed Simulation. However, the HLA standard does not provide any graphical language for defining the simulation scenario. This point could be interesting for the reusability problematic. In our case, the goal is to model and simulate business process (BP). A BP is a set of interrelated activities that are executed by one or more organizations working together to achieve a common business purpose (K L [START_REF] Ko | A Computer Scientist's Introductory Guide to Business Process Management (BPM)[END_REF]. Several modeling languages were introduced for defining industrials workflows, but Business Process Model and Notation (BPMN) is most widely adopted by users. The Business Process Model and Notation (BPMN) standard is a graphical notation for specifying business processes. It could be a viable solution to represent how Federates interact through a Federation. Using this standard as an HLA execution scenario will helps users to build simulation and insure execution traceability. This approach follows Model Driven Architecture (MDA) principles since it allows to divide conceptual modeling and execution in order to simplify work for people with low skills in IT and HLA.

However, the HLA standard doesn't provide any graphical language for defining the simulation scenario. This point could be interesting for the reusability problematic. The Business Process Model and Notation (BPMN) standard is a graphical notation for drawing business processes. It could be a viable solution for representing how Federates relate to each other, throw a Federation. The use of this standard will serve as an HLA execution scenario and help users to build simulation and assure execution traceability.

The rest of the paper is organized as follows. Section 2 describes the different concepts and technological backgrounds of this work. Then, section 3 presents a brief study and discussion about the work related to the integration of BPMN standard with HLA standard. Section 4 discusses the detailed steps of the proposed framework and the reflection on how this approach can make the development of the HLAbased DS easier for Management Sciences. Finally, Section 5 is a conclusion of the paper.

BACKGROUND

This section introduces the different concepts used in the proposed framework for DS in management science.

Modeling and Simulation Interoperability

From a M&S process perspective, distributed simulation implies dealing with different subsystems forming a coupled problem which are modeled and simulated in a distributed way. Indeed, the different domains of expertise may have different M&S tool, modeled and implemented in different languages. Besides, some of these tools must be available only on some specific hardware. Interoperability processes are then required to synchronize these heterogeneous tools and manage exchanges of data amongst them.

Distributed simulation technologies are a paradigm to model dynamic, heterogeneous, and spatial distributed systems. They not only aim at speeding up simulations, but also serve as strategic technologies for linking simulation components of various types [START_REF] Chen | A Decoupled Federate Architecture for High Level Architecture-Based Distributed Simulation[END_REF]. There are several approaches in the field of M&S offering interesting solutions to the challenges of the interoperability of simulation models and their execution on distributed computing environment. Two of the most popular efforts going in these directions are Functional Mock-up Interface (FMI) and. HLA is an IEEE standard (IEEE 1516) for distributed computer simulation systems (IEEE Computer Society 2010a). In the HLA standard a distributed simulation is called Federation (see Fig. 1). A Federation is composed of several HLA simulation entities, called Federate, which can interact among them by using the Run-Time Infrastructure (RTI). The RTI represents a backbone of a Federation execution and provides a set of services to manage the communications and data exchange among Federates. In this work, we adopted the HLA standard to simulate our system in a distributed environment.

High Level architecture (HLA)

In the computer simulation domain, distributed simulation is one of the most useful approach to reuse and run together different applications. Indeed, it consists of several co-running components (often associated with one or more functions) which can be processed by different processors. All of these components are part of a single execution which can be located on different computers / servers, hence the term "distributed". This concept of functions relocation makes the loads distribution possible on different machines, increasing the efficiency of a program.

One of the advantages of distributed simulation is to solve interoperability problems. Interoperability is the interactions ability between systems. This issue appears when several highly dissimilar systems (by their internal structure, exchanged data format, or semantic data) must communicate. The interoperability issue must be considered if interactions are at data level, service level or process level [START_REF] Zacharewicz | Multi Agent HLA Entreprise Interoperability (Short-Lived Ontology Based)[END_REF].

Indeed, in distributed simulations, the components are modular. They can have a heterogeneous architecture and exchange different kind of structured messages. This enables the solving of interoperability problems.

HLA defines a framework which allows the creation of global execution. This framework defines how to create a "global" simulation, which is made of several distributed simulation participants. Distributed simulation participants are called federates, they can communicate with one another. It was originally created by the Office of Defense Modeling and Simulation (DMSO) of US Department of Defense (DoD) to facilitate the assembly of stand-alone simulations with a different architecture. The original goal was the reuse and the interoperability of military applications, simulations and sensor. This standard is designed to resolve interoperability and reusability issues between software components. Another interesting aspect of this specification is the synchronization aspect. It allows to dynamically manage interoperability issues with simulations exchange messages: it must be ensured that messages are sent at the right time, in the right order, and that they do not violate causal constraints. To do this, various systems for synchronization of processes and time management are proposed by HLA. According to the HLA standard, each simulation participating to the application is called "federate". A classical HLA federate consists of a simulation model and local RTI component (LRC). The simulation model is a physical, mathematical, or logical representation of processes and systems. These entities can communicate with each other through a Run-Time Infrastructure (RTI). It is the RTI which manages the federation, authorizes federates to communicate or not, and provides various services such as time management, file or data exchange, etc. The FOM file is a XML file which describes interactions/communications between federates (see Figure 1).In our application case, this notion of distributed simulation will be tackled by the HLA (IEEE Computer Society 2010b). It will support the specification of our software architecture.

Business Process Model and Notation (BPMN)

BPMN is a graphical notation for drawing business processes. BPMN has been proposed by the Business Process Modelling Initiative (BPMI) and is currently maintained by the Object Management Group (OMG 2003) which provides this standard for IT and business actors. It is frequently supported by a computer program which enables a quite easy graphical description of complex processes. It provides a standard notation which is easily understandable by all stakeholders; also bridges the communication gap frequently occurring between business process design and implementation. Nowadays, BPMN becomes widely used by different organizations, as it is easy to learn, and powerful enough to depict the potential complexities of business processes [START_REF] Sbayou | Agent Based Modeling Architecture with BPMN and DEVS Network[END_REF].

STATE OF ART

As recalled previously, HLA is a well-known standard. It is described in different specification books, and it is used since 1996. One of them (HLA Object Model Template (OMT) (IEEE Computer Society 2010b) describes how interactions must be done between federates through mechanism of Subscribe (read) and Publish (write). Those communications are described by SOM and FOM XML files. However, there is no simple way to describe federate behavior inside the federation: each federate is autonomous. They can publish information, subscribe information, at any time. The only way to control them is to (re)develop them.

However, HLA components are still reusable according to the HLA Federation Development and Execution Process (FEDEP) (IEEE Computer Society 2010c) which has been recently integrated into the more general DSEEP (Distributed Simulation Engineering and Execution Process) standard). DSEEP uses seven-step process to guide the development of the simulation system as described:

- Federates are autonomous, but must be reworked in order to be reused. This can be an advantage, but sometimes, in a highreusability environment, this can be an issue. Several papers have already noticed the need of using graphical standard notation like BPMN in HLA domain. Despite this finding, there are few studies in the academic literature which have specified DS to simulate complex systems by graphically modeling the different component and their interaction of the DS project.

In industrial domain, visual interactive modeling environments are widely used. [START_REF] Taylor | Guidelines for Commercial Off-the-Shelf Simulation Package Interoperability[END_REF] find that, in DS domain, HLA is mainly used and the absence of graphical language can be problematic. Indeed, it can be easy to lose track regarding exactly what is wanted to occur between interoperating models. In that paper, the authors offered a set of interoperability reference models which can be used as guidelines to simplify interoperability process [START_REF] Taylor | Guidelines for Commercial Off-the-Shelf Simulation Package Interoperability[END_REF]. All those papers have different goals, but they all demonstrate the importance of using BPMN as standardized graphic user interface in order to simplify the HLA development.

The aim of this paper is different than all the others because it proposes a new concept: the explicit specification of (and potentially restriction) of HLA execution process, in order to achieve that goal. The proposed approach uses one federate as Master, controlling the others as Slaves. The Master federate read a BPMN diagram given as in input, and orchestrate all federates like it is described by the BPMN diagram.

CONTRIBUTION

Towards a formalization of the execution process of the HLA-based distributed simulation

The use of graphical modeling, in particular BPMN standard, to define and model part of distributed simulation process (Design Simulation Environment and execution scenario) has several benefits: (1) it shows R&D projects and requirements in context rather than in isolation;

(2) it allows specialists to define in a unified and standardized way the execution process of the simulation, so that everyone in an organization can understand the objectives of a simulation; (3) execution traces of programs (Federation development) can be easily viewed and analyzed; (4) it creates a bridge which reduces the gap between the HLA code level and the corresponding BPMN processes [START_REF] Falcone | Engineering Systems by Combining BPMN and HLA-Based Distributed Simulation[END_REF]. Moreover, there is a need to improve the traceability execution process in HLA environment. Indeed, each federate is autonomous and it is not possible to anticipate (or plan) any execution scenario: each federate is evolving at its own pace and the final user cannot capture the overall behavior (or the HLA DS execution process). The use of BPMN standard to control execution process would be a solution for this issue. In addition, numerous BPMN tools can support the process of software development by offering a variety of editors and code generation components. This allows us to automatically generate the component responsible for the simulation process through a BPMN diagram.

The articulation of these two standards enables the automatic generation of executable code which can be packaged in global DS system. A second way would be to build the HLA federate component (master) which has the responsibility to orchestrate the steps of execution process through the interpretation of a BPMN diagram and controlling the data exchange between the Federation (Figure 2). This proposition enables an approach towards MDA, with the use of BPMN Model in the one hand, and the separated execution of it in the other hand. According to HLA standard, each federate can communicate with Object or Interaction class through Subscribe and Publish mechanism. Thanks to that, they can share simple and complex types of data. However, any document or method are provided by the standard to specify which Distributed Simulations are connected to which others. By using a BPMN diagram as DS orchestration, we can model federate execution scenario (Fig. 2) and interaction that they have with others entities (Fig. 3).

In the Fig. 3, we propose to model HLA federate interactions with BPMN data associations flow. As we can see in the above figure, Federate A will publish an Object Class, which will be read by Federate B. The author of the DS Orchestration document can also add BPMN comments in order to, precise which type of data are exchanged and link the FOM file.

Experiment

From a technical point of view, after a few tests, we made an example for our proposition. Our study case is a solar power plant mobile factory [START_REF] Gorecki | Using High Level Architecture to Combine Simulations in Company Context Mobile Factory[END_REF]. The goal of this simulation is to estimate production cost of a solar power plant in using several distributed simulations. As we can see on Fig. 4, we simulate the assembly of a power plant fragment. As represented in the BPMN DS Orchestration diagram, each assembly station is autonomous simulations, they are part of an HLA federation. These 5 assembling posts are using a single production line which is the solar panels chassis. Each simulation will add to the chassis a new part. The first simulation (1) bring to the production line a new solar panel chassis. It will be created depending on several parameters. This simulation also takes risks in account and can build a chassis with dimensions defect. Those conceptions errors are generated randomly. The second simulation is about the solar receiver (2), it place a solar reflector on the chassis in order to receive solar ray. The (3)is linked to the (2) it will consiste in place tube containing coolant liquid. The Reflector Simulation (4) concern assembling on the production line mirrors for reflecting solar ray in the solar receiver. Finally, the last simulation ( 5) check for all previous simulations errors. If one of them made a mistake, the car will be rejected.

Otherwise, it will be expediate on the power plant.

During the simulation, all federates interact with Production Line (PL) which is represented by (Fig. 5) a MySQL Database. Each Distributed Simulations read and write informations in that external entity representing the Production Line. During the execution course, each federate successively access to the database and write the result of their own simulations. In the final step, the last simulation will compare information written in database to the customer needs. If errors are detected, the car is rejected, otherwise, the product is expedited.

The graphic below (Fig. 6) describes technical architecture of the proposition according to 3 technical layers. The second layer (which correspond on Fig. 6 by cross hatch rectangles) represent an API which implements the master/slave mechanism described in the previous section. This layer will, from the Master federate point of view (gray rectangle), use publish and subscribe RTI functionalities to send: run, stop, and freeze orders to the federates (white rectangle), according to the DS Orchestration diagram. From the other federates point of view, this layer will freeze the local simulations at t = 0 (as described on Fig. 4) and put them in stand up status. Still from the slave federate's point of view, the API will be in charge to receive, run, stop and freeze orders from the master federate. Those orders will be applied on the local runtime simulation. The master federate will read the xml file that describes the BPMN diagram and address to each federate run, stop, freeze orders through the BPMN orchestration API layer.

This experiment allows us to demonstrate the reusability increase of our proposition. With the BPMN orchestration API, we can simply modify a simulation execution process with a graphical standard. In our example, the engineer can modeling federates behaviors through BPMN standard, and directly execute it without modifying code.

CONCLUSION

In distributed Simulation, IEEE HLA is a widely used standard because of its capacity to solve heterogeneous issues and/or its reusability potential. Federation enables to define a set of entities (federates) representing different solutions for a large problem. Literature reported that each federate is autonomous, have its own architecture but the design of federates' orchestration before simulation time is not easy an easy task. This papers is a contribution to facilitate the specification of federates communication making more explicit the publish and subscribe steps. In other words, it attempts to give a more clear and explicit support to describe the desired sequence of execution between the different federates. This contribution specifically finds its interest, with the complexity of the system to model, where designing a complete distributed simulation is a challenge. An example has been introduced to illustrate the contribution, a distributed simulation can be orchestrated with a BPMN diagram. We consider that the adoption of Business Process Modeling and Notation standard as graphical notation for defining HLA execution scenario will help non-specialists of M&S to define in a unified and standardized way the execution process of the simulation and also will facilitate DS execution process analysis after simulation run.

Future research efforts will be devoted to the definition of how communication (publish/subscribe) protocol are defined in our proposition. The BPMN Orchestration will use message flow to indicate publish and subscribe exchanges but must be developed to precise the category of data to be exchanged for instance.

Fig. 1 .

 1 Fig. 1. HLA Architecture diagram.

Fig. 2 .

 2 Fig. 2. Combining HLA-based Distributed Simulation and BPMN.

Fig. 3 .

 3 Fig. 3. Interaction between federate with BPMN data association flow diagram.

Fig. 4 .

 4 Fig. 4. BPMN and UML sequence flow diagram for solar panel production line.

Fig. 5 .

 5 Fig. 5. Production Line (PL) UML class diagram.

Fig. 6 .

 6 Fig. 6. Layering technical architecture. The first layer (RTI, FOM, and HLA Interfaces) represent the HLA standard architecture, which is not modified. All HLA and RTI functionality are still available in this application (this allows us to say the HLA standard is still respected), but in a upper layer, we propose to reduce RTI functionality in order to simplify the scenario's definition step. All federates contain a first layer HLA Interface -LRC which implements Local RTI Component enabling communication with RTI, and we


Fabrice Chauvin
email: fabrice.chauvin@meteo.fr

Sébastien Denvil

Changes in severe indices as simulated by two French coupled global climate models

Extremes are assessed here in an attempt to validate the two French models in their representation of the second part of the 20 th century, using different sources of gridded observational datasets. Models show some ability to simulate extremal behaviour of the climate even if discrepancies are noticeable between models and observations. These may be partly due to the low resolution used for the present study simulations. Extreme indices, calculated using the STARDEX (STAtistical and Regional dynamical Downscaling of EXtremes for European regions) methodology, are investigated in different IPCC (International Panel on Climate Change) scenarios performed by the French community. Investigation of 21 st century severe indices simulated in these simulations

shows some interesting features. In some parts of the world, extreme temperatures experience a more rapid increase than the mean, suggesting that the Power Density Function (PDF) may not only be shifted toward higher temperatures but also changed in its shape.

Extremes of precipitation also experience a change toward more intense precipitation events in winter and longer dry events in summer. Approaching future changes in extreme indices through their relationship to mean annual temperature may be a useful approach in multi-model studies, since it provides a measure of the sensitivity of extremes to warming conditions in these models.

Introduction

The impact of greenhouse gas (GHG) concentrations on the global temperature has been apparent for several years in observations [START_REF] Jones | Hemispheric surface air temperature variations: a reanalysis and an update to 1993[END_REF][START_REF] Peterson | Homogeneity adjustments of in situ atmospheric climate data: a review[END_REF]and Jones et al. 2001) and future predictions generally indicate an accelerated rate of warming with increasing GHG concentration [START_REF] Houghton | Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (IPCC)[END_REF]. By cumulating uncertainties due to the IPCC (International Panel on Climate Change) GHG scenarios and the diversity of different atmosphere-ocean coupled models used for prediction, the expected global warming for the end of the century is estimated at between 1.5 and 6°C [START_REF] Houghton | Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (IPCC)[END_REF]. Modelling uncertainties are essentially due to differences in parameterizations between models, among which cloudiness is probably the most important [START_REF] Gates | An overview of the results of the Atmospheric Model Intercomparison Project (AMIP I)[END_REF]. In terms of impacts, a major effect of global warming on societies may arise from associated changes in severe events, since populations and infrastructures are very sensitive to extremes of climate. As a consequence of global warming, the shift of the temperature distribution toward higher values implies that present severe temperatures may become quite usual in the future.

One consequence of this shift is that physiological thresholds may be exceeded more frequently than today, with dramatic human and natural consequences. In the French IMFREX (IMpacts des changements anthropiques sur la FRéquence des phénomènes eXtrèmes de vent, de température et de precipitations) Déqué shows that the probability of occurrence of a summer day with T x over 35°C is multiplied by a factor of 5 to 10, over France, in a A2 scenario performed with ARPEGE/Climat GCM (see website on http://medias.dsi.cnrs.fr/imfrex/web/index.fr.php). There is strong evidence of observed trends in 20 th century mean temperatures [START_REF] Jones | Adjusting for sampling density in grid box land and ocean surface temperature time series[END_REF] according to monthly mean reconstructions using a large number of global observing stations. The necessary homogenization of datasets is not as easy for daily observations as for monthly ones, since the technology lies on spatial similarity, which is not always verified for daily observations, given their variability [START_REF] Mestre | Méthodes statistiques pour l'homogénéisation de longues séries climatiques[END_REF]. Dealing with extremes in climatic simulations requires particular techniques, based on statistical models, which are used to describe distributions of extreme values.

The most popular is the Generalized Extreme Values (GEV) model (Coles 1999), which was used by [START_REF] Kharin | Changes in the extremes in an ensemble of transient climate simulation with a coupled atmosphere-ocean GCM[END_REF] to qualify changes in extreme events in a global scenario. The drawback of this approach is the scarcity of the extreme event under consideration. This makes the method inadequate for short datasets of observations. More sophisticated methods like the Generalized Pareto Distribution models [START_REF] Hosking | Parameter and quantile estimation for the generalized Pareto distribution[END_REF]) may be used but another problem occurs with this kind of approach, linked with the accuracy of the threshold used in a future climate or the independence of variables. Another way to approach extreme sensitivity to climate change is to consider slightly less extreme events, i.e. those events that are located far from the mean climate but more likely to occur than outlying extremes. These may be qualified as severe events. This was the basis of the STARDEX (STAtistical and Regional dynamical Downscaling of EXtremes for European regions) project (http://www.cru.uea.ac.uk/cru/projects/stardex/), by the definition of 57 indices associated with severe conditions of temperature and precipitation over European regions. [START_REF] Frich | Observed coherent changes in climatic extremes during the second half of the twentieth century[END_REF] have documented changes in ten of the 57 severe indices during the second half of the 20 th century and this subset is part of the IPCC model outputs required for the Fourth Assessment Report (FAR), which is to be edited in 2007.

As contributors to FAR, the Centre National de Recherche Météorologique (CNRM, Météo-France) and the Institut Pierre et Simon Laplace (IPSL, Centre National de Recherche Scientifique) produced these indices for all the simulated scenarios. This study will present the evolution of some of the severe indices calculated, during the 20 th and 21 st centuries, according to IPCC commit, B1, A1B and B2 scenarios [START_REF] Nakicenovic | Special Report of the Intergovernmental Panel on Climate Change[END_REF]. Models and simulations will be presented in section 2.

Validation datasets will be presented in section 3. In section 4, STARDEX indices will be presented and their future changes assessed. Thus, section 5 will discuss their sensitivity to mean annual temperature. We will conclude in section 6.

Models and simulations

The CNRM coupled configuration (CM3)

The ARPEGE-Climat atmospheric model originates from the ARPEGE/IFS (Integrated Forecast System) numerical weather prediction model developed jointly by Météo-France and European Center for Medium-range Weather Forecast (ECMWF). It is a spectral atmospheric model with a hybrid σ-pressure vertical coordinate. Since the first release of the ARPEGE-Climat model [START_REF] Déqué | The ARPEGE/IFS atmospheric model: a contribution to the French community climate modeling[END_REF]), many developments have been included, both dynamical and physical. Here we use the third generation of ARPEGE-Climat model [START_REF] Déqué | Documentation ARPEGE-CLIMAT[END_REF]. The main difference compared to former versions is the use of a two time-level semi-lagrangian numerical integration scheme with a 30 minute time-step. The physical package includes the turbulence scheme of [START_REF] Louis | A short history of the operational PBLparameterization at ECMWF[END_REF], the statistical cloud scheme of [START_REF] Ricard | A statistical cloud scheme for use in an AGCM[END_REF], and the mass-flux convective scheme with Kuo-type closure of [START_REF] Bougeault | A simple parameterization of the large-scale effects of cumulus convection[END_REF]. The radiative scheme is derived from [START_REF] Morcrette | Impact of changes to the radiation transfer parameterizations plus cloud optical properties in the ECMWF model[END_REF] and is activated every 3 hours. More details about the physics of the model can be found in Geleyn et al. (1995). At the Earth's surface, the Interaction Soil-Biosphere-Atmosphere (ISBA) land surface scheme [START_REF] Noilhan | A simple parameterization of land surface processes for meteorological models[END_REF]) is used to provide boundary conditions for the computation of surface fluxes (Mahfouf et al. 1995). Although it contains the basic physics of land surface processes, the ISBA scheme only needs a few parameters depending on soil and vegetation.

Vegetation types are derived from the 1-km resolution ECOCLIMAP database [START_REF] Masson | A global database of land surface parameters at 1-km resolution in meteorological and climate models[END_REF] which was developed at CNRM (Centre National de Recherches Météorologiques). The ISBA scheme has four prognostic variables for liquid water (see [START_REF] Douville | Assessing the influence of soil moisture on seasonal climate variability with AGCMS[END_REF] for a complete description of the ISBA scheme).

For the IPCC simulations, ARPEGE-Climat has been coupled with oceanic OPA [START_REF] Madec | Opa 8.1, ocean general circulation model reference manual[END_REF]) and sea-ice GELATO (Salas-Mélia 2002) by the OASIS coupler [START_REF] Terray | The OASIS coupler user guide version 2[END_REF]. The atmospheric grid is in T63 spectral truncation (with a collocation grid of 128x64, equivalent to a 2°8x2°8 resolution) and the oceanic grid on a 182x152 resolution. The fully complete description of the IPCC configuration of the coupled model can be found in [START_REF] Salas-Mélia | Description and validation of the CNRM-CM3 global coupled model[END_REF]. The CNRM coupled configuration wil be further referenced as CM3 (for Climate Model version 3).

The IPSL coupled configuration (MC2)

The climate model IPSL-CM4 [START_REF] Marti | The new IPSL climate system model: IPSL-CM4[END_REF], used for IPCC simulations, is composed of the atmospheric LMDZ-4 [START_REF] Hourdin | The LMDZ4 general circulation model: climate performance and sensitivity to parametrized physics with emphasis on tropical convection[END_REF], oceanic ORCA [START_REF] Madec | Opa 8.1, ocean general circulation model reference manual[END_REF], land surface ORCHIDEE [START_REF] Krinner | A dynamic global vegetation model for studies of the coupled atmosphere-biosphere system[END_REF]) and sea-ice LIM [START_REF] Fichefet | Sensitivity of a global sea ice model to the treatment of ice thermodynamics and dynamics[END_REF]) models, coupled by the new OASIS coupler [START_REF] Valcke | Spatial and temporal characteristics of heavy precipitation events over Canada[END_REF]). The direct and first indirect effects of sulphate aerosols have been parameterized [START_REF] Pham | Changes in atmospheric sulfur burdens and concentrations and resulting radiative forcings under IPCC SRES emission scenarios for 1990-2100[END_REF]. In contrast to ARPEGE-Climat, the dynamical part of the atmospheric model is based on a finite-difference formulation of the primitive equations of meteorology [START_REF] Sadourny | January and July performance of the LMD general circulation model[END_REF]. The grid used in this set of simulations is a 96x72 longitude/latitude (corresponding to a 3°75x2°5 equivalent resolution). The physical package includes an improved Emmanuel's convective scheme (Emmanuel 1991, Bony and[START_REF] Bony | A parameterization of the cloudiness associated with cumulus convection; evaluation using TOGA COARE data[END_REF]) and a representation of clouds through a probability density function of sub-grid scale total water [START_REF] Le Treut | Sensitivity of an atmospheric general circulation model to prescribed SST changes: feedback effects associated with the simulation of cloud optical properties[END_REF]. The effects of mountains are derived from [START_REF] Lott | A new sub-grid scale orographic drag parametrization: its formulation and testing[END_REF] and [START_REF] Lott | Alleviation of stationary biases in a GCM through a mountain drag parametrization scheme and a simple representation of mountain lift forces[END_REF]. Turbulent transport in the planetary boundary layer is treated as a vertical diffusion with an eddy diffusivity depending on the local Richardson's number [START_REF] Laval | Land surface processes in a simplified general circulation model[END_REF].

The surface boundary layer is treated according to [START_REF] Louis | A short history of the operational PBLparameterization at ECMWF[END_REF]. Additionally, a tuning of the boundary layer scheme follows Krinner et al. (1997) and [START_REF] Grenier | Ocean-atmosphere interactions and climate drift in a coupled general circulation model[END_REF]. The IPSL coupled configuration will be further referenced as MC2 (for Modélisation Climat-Cycles project).

Validation datasets

Monthly datasets of several variables have been compiled in the past and it is now easy to find a number of gridded global datasets of classical observed variables, such as temperature or precipitation. Homogenization techniques have been developed to provide long-time series at many locations worldwide, and it allows the construction of global gridded datasets long enough for validation purposes.

When calculating severe events at the annual frequency, daily data are needed. Ideally, complete and homogeneous long-time series of observations are required but homogenization techniques for daily data are not well developed compared with those for monthly data [START_REF] Mestre | Méthodes statistiques pour l'homogénéisation de longues séries climatiques[END_REF] and compilation of daily gridded datasets can be an intensive task. In the present study, three sources of observation-derived products were used, with an incomplete coverage of the world and available for only a few variables. The first dataset contains the daily minimum/maximum temperatures (T n /T x ) and precipitation for the North-American continent over the period 1951-2001 and was compiled by [START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF]. This dataset is important since it is the only dataset that allows us to calculate all the severe indices which will be used in this study. The drawback is that it is limited to the North-American continent. The second dataset is a new quasi-global T n /T x daily dataset covering the 1946-2000 period. It was compiled by a team from the Met Office Hadley Centre for Climate Prediction and Research [START_REF] Caesar | Large-scale changes in observed daily maximum and minimum temperatures: Creation and analysis of a new gridded data set[END_REF]. This dataset provides near-global coverage but does not currently include precipitation data. Nevertheless, it is a valuable product for model validation. Finally, the third dataset only provides the number of frost days, for the period 1902-2002, as an empirical derivation of monthly minimum temperature, obtained as the mean temperature minus one-half diurnal temperature range [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF]. Although this calculation is quite empirical and does not include any station observed ground frost days, it represents a nonnegligible source of validation data for model simulations. Moreover the North American continent and eastern Europe are well covered with stations all along the period of observations. Western Europe, nevertheless, is only covered during the second part of the20 th century (see figure 3 of [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF]. Since the three datasets mentioned above cannot give a globally complete image of extreme behaviour of the atmosphere, we decided to focus on two continental regions, North-America and Europe, which have the densest observational networks.

Since the object of this study is to validate the extremes in the French scenarios, and as model climatologies should be assessed in other papers, we do not show such climatologies to avoid repetition. However, even though the two models tend to present their own biases, the global response in temperature is comparable between the two sets of French scenarios.

STARDEX indices

The European STARDEX project, supported by the European Commission (Contract no: EVK2-CT-2001-00115), defined a sub-set of 57 extreme indices as interesting variables to look at for characterising the extreme behaviour of the climate [START_REF] Haylock | Interannual variability of European extreme winter rainfall and links with mean large-scale circulation[END_REF]. Among these variables, ten were selected as IPCC diagnostics for the FAR. As part of the French contribution to the FAR, the STARDEX indices were calculated for the scenarios provided by CNRM and IPSL. Given the differences in the mean response between the two sets of scenarios (not shown here), some noticeable changes in the extreme indices may be expected.

In a first step, geographical changes for the end of 21 st century will be presented for four kinds of severe indices taken from those required by IPCC. These four indices are the annual number of frost days (TNFD), the summer heat wave duration index (HWDI), the number of winter heavy precipitation days, i.e. when precipitation is over 10 mm (PN10MM), and the summer maximum number of dry days, i.e. when precipitation is under 1 mm (PXCDD). These indices were chosen for their representation of different kinds of severe events that may induce damageable consequences for societies and human safety. From geographical changes, different regions will be selected for their homogeneous response and indices will be averaged over these regions to study their temporal evolution as well as their sensitivity to 21 st century expected warming.

21th century geographical change

Figure 1 shows the geographical changes between the end of both 20 th and 21 st century, of the annual TNFD index, for the two A2 scenarios of CM3 and MC2. As suggested by figure 1,MC2 shows a larger change than CM3, particularly over Canada, where decrease can reach more than 90 days on western coast and Alaska. Over this coast, CM3 indicates changes from 10 to 60 days from North to South. This is a very strong change since it corresponds to up to 3 months more when lands should be out of frost, with a large impact on the hydrological cycle as well as ecosystems. A big difference also exists over Scandinavian countries where MC2 shows a larger decrease than CM3. For the other places, changes are similar, particularly the position of the southern limit of changes that do not exceed 10 days. CM3, however, shows a slightly southernmost position of this limit over Mexico and Arabian peninsula.

The impact of anthropogenic warming on the length of heat waves, represented by the summer HWDI can be seen in figure 2. HWDI is the maximum number of consecutive days for which T x is at least 5°C higher than the 1961-90 normal. Except over the high latitudes in CM3 and ITCZ in MC2, an increase is noticeable over all parts of the world with higher intensities evident in CM3 over the countries surrounding the Mediterranean sea, the central United States and western Canada, while MC2 shows more homogeneous change, except over Northern Canada, Northern Europe and former USSR. These patterns may be attributed to two distinct responses of the surface to changing climate. Anthropogenic warming forces a shift in the temperature distribution which implies, due to its definition, a substantial increase in HWDI. If temperatures are warmer in the future than in the present without changing the reference threshold, the number of days exceeding the threshold will be systematically higher, leading to a higher probability of more consecutive days over this threshold. In addition to this mechanical effect, changes in precipitation may add a negative feedback which leads to an increase in HWDI where summer precipitation is reduced. This feedback is explained in Douville (2005) by the double effect of reduced precipitation on decreased soil moisture as well as a decreased cloud forcing. This precipitation feedback will be discussed later on, when interpreting the non-linear relation between HWDI and mean temperature, in section 5.

Figure 3 shows changes in winter PN10MM for the CM3 and MC2 A2 scenarios. The two simulations show a fairly similar response to global warming for this index, with an increased activity of severe precipitation over northern mid-latitudes, specially over Europe and Canada, as well as in the ITCZ and a decrease over tropical latitudes and Mediterranean countries, except over Spain and Australia for. North America changes are stronger in MC2 and European ones in CM3.

Mid-latitudes changes are probably due to an enhanced baroclinic activity which may be expected in a warmer climate or, at least, a moister associated atmosphere, leading baroclinic systems to produce more rainfall for the same activity. Tropical decrease may be a result of reduced soil moisture associated with more dryness. This increased dryness is particularly marked in summer when the PXCDD index experiences an increase over a major part of extra-tropical latitudes (figure 4). The two simulations differ only over the western coast of the USA, where CM3 indicates an increase while MC2 indicates a decrease, Arabian peninsula, where only CM3 indicates an increase and north-western Indian peninsula where only MC2 show a decrease which may be associated with an enhanced monsoon activity.

Over North-African continent, CM3 shows a decrease of dryness in the western and an increase in the eastern part. It is in agreement with changes in mean precipitation field associated with African monsoon (not shown). The two simulations agree on a decrease of dry sequences in the ITCZ, in agreement with its enhanced activity. It can be noticed, in both simulations, that regions where PXCDD strongly increase significantly are also associated with particularly increased HWDI, confirming the strong link between heat waves and lack of precipitation. This also suggests that precipitation represents a strong feedback on extreme temperatures and that the ability of models to simulate rainfall should be enhanced to better predict the impact of anthropogenic warming on these extremes.

Regional average validation and evolution

Although STARDEX indices (SI in the following) have been defined as station-dependent and give, by essence, local information on extreme behaviour of the climate, one may consider that such indices are representative of the surrounding region, as represented by a gridpoint in an atmospheric analysis. This is probably true for temperature related indices, since this variable is spatially homogeneous. It is more questionable for precipitation related indices, although winter heavy precipitation is, most of the time, associated with synoptic scale systems and summer dryness is generally widespread over countries. In order to assess the impact of gridding process on the calculation of SI, one experiment may be considered. First, SI should be calculated, as it is done in this study, from daily gridded analysis such as the recent T x /T n dataset covering the period 1946-2000 produced at Met Office [START_REF] Caesar | Large-scale changes in observed daily maximum and minimum temperatures: Creation and analysis of a new gridded data set[END_REF]. On an other hand, apply the gridding process to SI calculated from each observing station. The comparison of the two resulting SI should give some information on the gridding impact on the extreme behaviour of the atmosphere. Nevertheless, it is not under the scope of this study to assess this point and it is hypothesized that daily gridded data are able to capture severe events in the same way as station observations do. At the regional scale (~5000 kms by opposition to local scale which is ~100-500 kms) averaged indices provide interesting information on the ability of the models to represent severe events, although we found it necessary to limit the spatial extension of the regions in order to avoid melting different climates in a same region. In this study, five regions were selected for their homogeneous response of indices. These regions have been reported on figures 1 to 4 as red boxes. Boxes were distributed over the 4 figures for more clarity. The five selected regions are Alaska (58-70°N, 165-105°W), Canada (38-58°N, 130-70°W), USA (28-38°N, 120-75°W), Europe (45-60°N, 15°W-45°E) and Mediterranean countries (28-45°N, 15°W-45°E). Figure 5 shows the time evolution of averaged TNFD over the five regions for both CNRM and IPSL A2 scenarios along the 240 years of simulation. Also represented are the equivalent averages for the three kinds of observed dataset over North-America and two kinds over Europe (Eischeid dataset is available only over North-America). Given the large variability in observations, for which differences may reach 50 days over Canada, the two models appear to simulate quite reasonably the index. While the two simulations are in a good agreement over Europe, the CM3 tends to be colder than MC2 over North America, resulting in a difference of respectively 20, 30 and 40 days for Alaska, Canada and USA. Over Alaska and Canada, TNFD decrease more quickly in MC2 than in CM3, leading to a difference of 60 days at the end of 21 st century. Over Europe, the two scenarios are similar in their present TNFD (~160 days) as well as their decreasing rate, leading to 80 days at the end of 21 st century.

Mediterranean countries are not caught in the same way in the two scenarios since CM3 shoes 20 more days than MC2 at the beginning of the period. The decreasing rates are different such as it results in a common 15-20 days at the end of 21 st century. Concerning observations, a decrease is noticeable in all the regions during 20 th century, giving some credit to the simulated decrease in models. Over Mediterranean countries, the Met Office dataset [START_REF] Caesar | Large-scale changes in observed daily maximum and minimum temperatures: Creation and analysis of a new gridded data set[END_REF]) even shows a decreasing shift between 1950s and 1960s which may be attributable to observation deficiencies. In both scenarios, the decrease is accelerated during the 21 st century, even if it is noticeable as soon as beginning of the 20 th . It should be noticed that MC2 is run with months of 30 days long, leading to years having 360-days instead of 365 or 366. We assume that the impact of this different duration of the year is negligible since the difference in total number of days is 1.4%.

The HWDI (fig. 6) shows a strong trend after year 2000 for the two scenarios, except over Alaska where CM3 keeps it constant, as suggested by figure 2. Before, the maximum length of hot spells does not reach 5 days in major regions, except over USA and Europe, in agreement with observations, and it can reach more than 60 days at the end of 21 st century, over the Mediterranean, in CM3. The increase in HWDI is associated with an increased variance, suggesting that warming keeps and even enhance the strong interannual variability which exists in the index. Nevertheless, although this increase in variance, low HWDI years at the end of 21 st century are still far higher than present ones. It seems that there is a threshold effect in HWDI, since its increase only begins at the end of the 20 th century while the T x warming begins earlier. This threshold is essentially due to the choice of the 90 th percentile calculation on the 1961-1990 period. This point will be assessed in the next section.

We will now focus on precipitation-related indices, one for strong events in winter (PN10MM) and the other concerning summer dry spells (PXCDD). These two indices can only be validated over North America since only the Eischeid's dataset provides daily precipitation observations. Figure 7 shows the time evolution of winter PN10MM for the five regions previously identified. The two models agree over Europe and the Mediterranean. They differ over the whole North America, where CM3 seems to be more realistic over Alaska and Canada. Strong winter precipitation events increase over Alaska and Canada, as well as Europe, for the two scenarios. The interannual variability is more marked over low than over high latitudes. USA and the Mediterranean do not show any marked evolution (except a slight increase over USA for CM3). Variance do not seem to change between the beginning and the end of the period.

Summer dry spells (fig. 8) are in good agreement with observations for MC2 over Alaska and Canada while CM3 underestimates the dry spell duration. It is more realistic than MC2, nevertheless, over USA. 21 st century evolution of PXCDD depends on latitude and model. MC2

shows a 4 days increase over Alaska while CM3 does not show any change. Both CM3 and MC2

show slight increase over Canada, USA and the Mediterranean. MC2 and CM3 differ over Europe with a stronger increase for CM3. There is no change in the interannual variability of both precipitation indices during the whole period of simulation. These two indices suggest that the hydrological cycle will be enhanced in the future, with stronger events in winter, and more dryness, in summer. These results have already been shown, for the ARPEGE model mean precipitation fields, in [START_REF] Gibelin | Anthropogenic climate change over the mediterranean region simulated by a global variable resolution model[END_REF]. [START_REF] Durman | A comparison of extreme European daily precipitation simulated by a global and a regional climate model for present and future climates[END_REF] found European increased winter heavy precipitations in both GCM and Regional Climate Model (RCM). [START_REF] Frich | Observed coherent changes in climatic extremes during the second half of the twentieth century[END_REF] found an increase, in the last 50 years, of pn10mm for a large part of Northern hemisphere. However, they found a decrease of PXCDD, in contradiction with our results. [START_REF] Kiktev | Comparison of modelled and observed trends in indices of daily climate extremes[END_REF] also found a decrease. The apparent inconsistency probably comes from sampling effect as well as choice of the period of evaluation. Figure 9 shows the temporal evolution of PXCDD averaged over Europe (top) and USA (bottom) on the 1950-2000 period. For USA, the averages from Eischeid's dataset have also been reported. The figure illustrates that the observed decrease during the second part of the 20 th century is well captured by MC2. CM3, nevertheless, shows a very slight increase which has nothing to do with the one observed in figure 8 between end of 20 th and 21 st centuries. Thus, one should be careful in interpreting observed trends on short timescales since they may be attributable to sample effects. Considering larger periods may change the conclusions about the warming effect on precipitation behaviour.

Sensitivity of indices to mean temperature increase

One question which may be interesting to assess is whether the extreme indices vary linearly with mean annual temperature, since the latter is often used as a measure of global warming. In the case of linear relation, an increasing rate may even be attributed to each index relatively to temperature change. We have seen in the previous chapter that the relation was not linear for HWDI. Figure 10 shows a linear relation of TNFD with mean temperature at the regional scale, over four of the five selected domains. The Mediterranean, nevertheless, present a non-linear decrease of frost days with mean annual temperature. In fact, linearity of the relation is apparent in the different scenarios commit, B11, A1B and A2, except where the number of frost days comes close to zero. Thus, the behaviour becomes asymptotic. No feedback seems to operate on the change of this variable. Of course, the relation between the decrease of frost days and the annual temperature may vary from one place to another, but, at the regional scale, and given that gridpoints have a similar behaviour, the two French models show similar sensitivities, even if MC2 shows an underestimation of approximately one month over USA. The decreasing rate is between 7-11 days/°C over the North American continent and ~13 days/°C for Europe. As it was said earlier, for the Mediterranean, the relation between number of frost days and mean annual temperature is not linear and the decreasing rates evolves from ~13 days/°C for lowest to 5 days/°C for highest temperatures. Those rates seem to be fairly realistic when compared with observations, even if CRU dataset shows a sensitivity that is quite different over Alaska. This may be an indication that the latter is too large, due to the way frost days are estimated in [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF]. Indeed, it results from a complex and non-linear relationship between frost days and minimum daily temperature. This relationship was calibrated with United Kingdom observations only and may not be accurate for highest latitudes. The Eischeid's dataset shows a slightly greatest decreasing rate compared with other observation sources over USA.. As expected, figure 11 shows a non-linear relation between HWDI and mean annual temperature, the former increasing more quickly than the latter. Figure 12 shows, for Europe (top) and the Mediterranean (bottom), the value of the 90 th percentile of T x relatively to annual mean temperature for both scenarios. For the Mediterranean, figure 12 agrees with Beniston and

Stephenson ( 2004) who found a linear relation between the mean and the 90 th percentile of summer T x in two Swiss stations, with a regression coefficient not far from 1 (1.18 for Basel and 0.94 for Säntis). Nevertheless, Europe shows a non-linear relationship in CM3 which suggests that extreme temperatures increase more quickly that the mean. It implies that non-linear processes act to accelerate the increase of the maximum temperature (or to limit the increase of the mean). Midlatitudes baroclinic processes may be such non-linear feedbacks. What is suggested here is that the length of hot spells, as defined by HWDI, may increase more quickly than mean temperature, resulting in more dramatic effects for mid-latitudes continental regions than suggested by only considering the increase in the mean temperature. The question that may arise, at this point of the discussion is whether this increase is the result of a change in the shape or scale of the T x distribution associated with the increase of the mean. To assess this question a new HWDI was calculated relatively to a varying 30-year reference, instead of the fixed 1961-90 normal as used in the STARDEX definition. Thus, if change in the T x distribution is limited to the first order moment, it should result in no change in the HWDI. It is an other way to ask the question of the extreme character of the climate. The severe events of the future climate may be calculated comparatively to present or future mean climate itself. In the second case, what is assessed is really the extreme character of the future climate. In the first case, this is a shift from extreme to normal conditions that is assessed, between present and future climate. Consequences differ in the two cases because the necessary adaptation of societies may not be the same. If changes appear in how climate extremes withdraw from the mean, structural changes of societies should take it into account. As an illustration of the non-linear effect of increasing temperature on extreme indices, figure 13 shows the new HWDI for the five regions previously defined. The global period has been reduced by 15 years at the beginning and the end, due to the calculation of the moving 30-year normal. Figure 13 shows that changes in the new HWDI are quite smaller than those of the previous formulation.

Nevertheless, even small, the trend is positive, especially over Europe, where the index evolves from 1.6 to 3.1 days along the period, essentially due to more frequent events in the 21 st century.

Trends in other regions are not so marked, but Alaska and Canada see their strongest events during the 21 st century.

To explain why hot waves length increases more quickly than mean temperature, one may consider the increase in dryness over mid-latitudes of North-America and Europe in all the future scenarios (figure 15). More dryness favours large diurnal amplitudes and maximum temperatures. The relationship between precipitation and temperature is complex since both fields may influence each other. Increasing temperature favours convection but enhanced precipitation will, in turn, act as a negative feedback on the temperature. The resulting equilibrium between the two variables may be sensitive to the kind of precipitation regimes encountered in a warmer climate. The sensitivity of precipitation indices to mean temperature shows a changing character between winter and summer seasons (figures 14 and 15). In winter, number of days with precipitation greater than 10 mm day -1 increases with mean temperature in northern and southern parts of both Europe and North America. However, no sensitivity is observed in the Eischeid's dataset, at least in the temperature range for which observations are available. On the other hand, summer dryness is also enhanced with increasing temperature, except for CM3 over Canada. This lack of sensitivity is also noticeable in figure 4, where Canada experiences no change in the PXCDD index. Observation can not account for such a sensitivity, even if an increasing rate of PXCDD change with temperature may be seen over the three North-American regions. Temperature range of observations is, nevertheless, too short to conclude in the existence of such a relation or not.

Conclusions

This study focused on severe indices as defined in the STARDEX project and asked in the IPCC diagnostics for the FAR. What is original, here, is to consider severe indices at the regional scale and to define large places where the behaviour of extremes seems to be homogeneous. As an illustration of the use of these averaged indices, two temperature-related and two precipitationrelated indices were presented, as observed and simulated by the two French CNRM and IPSL models. Although there are some differences in present climate modelling of the indices, the two models agree in their relationship with mean temperature as well as its future evolution. If the linear relationship between mean temperature and number of annual frost days suggests, as expected, a dramatic decrease of frost days in the future, the non-linearity of the relationship between mean temperature and hot spells is even more worrying since hot spells could increase far more quickly than the expected mean warming simply suggests. Such a non-linear relation is found over Europe for CM3 while the other regions show linear relations and a fairly similar rate of increase for mean annual temperature and 90 th percentile of maximum temperature. For these regions, HWDI increases principally due to a mechanical shift of the mean temperature distribution. Thus, HWDI, by its non-linear definition, grows more quickly than the mean. For Europe, this is not exactly the case, since the 90 th percentile already grows non-linearly with the mean. So, to understand changes in European HWDI, a change in shape and scale of the temperature distribution must be considered additionally to its shift. We assume that this is due to interactions with moist processes. Weak linear relationships exist between precipitation indices and temperature, at the regional scale, although a tendency can be deduced from future scenarios, with increases in both winter heavy precipitation events and summer dry spells. This is coherent with an increase in the mean annual water cycle already found in other studies [START_REF] Douville | Sensitivity of the hydrological cycle to increasing amounts of greenhouse gases and aerosols[END_REF]. For summer dry spells, the apparent incoherency between scenarios, which show an increase of PXCDD between present and future climate, and observations, which show a decrease over the last 50 years, may be due to a sampling effect. Indeed, if the period of scenarios is limited to the observation one, there is no more discrepancies, at least for IPSL scenario.

The way to relate indices to mean temperature may be a useful tool for modelling validation purposes. On the same graph, one may see the biases in both model temperature and/or precipitation indices as well as departures from observations in the increasing/decreasing rate of change relatively to temperature warming. In addition to the future changes in the extreme indices, these graphics bring additional information on their rate of change, highlighting those which are the most sensitive to warming and should be, thus, the focus of attention. Moreover, these graphs are good indicators of changes that may occur in the relationship between extremes and mean temperature, due to the different feedbacks acting in a warmer climate. This approach do not pretend to assess extreme changes in all their complexity, especially where changes occur in scale and shape of daily variables distributions. Nevertheless, it is evident that there is some spatial coherency for severe indices which allow to condense the information provided by scenarios. In a multi-model intercomparison, such as the one that the actual IPCC exercise undertakes, such integrated approach can have some utility. Of course, station-dependent detailed studies are still needed to understand the exact relationship between climate and its extremes, and it should be clearly assessed with all the known statistical tools. But it is also useful to recognize that climate presents some spatial coherency allowing regional extrapolation which may be useful for policy makers. Further studies may address the geographical distribution of changing rates of extremes relative to mean temperature and highlight regions to pay attention for. But the limitation of this approach is that it may only be applied to indices which vary linearly with mean temperature. Observations are plotted as full triangles [START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF], stars (Caesar et al. 2005) or empty squares [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF] and lines are for CM3 (dashed) and MC2 (dotted) 20 th century+A2 scenario simulations. Observations [START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF] are plotted as triangles and regression line is solid. Vertical axis represents the number of days. Observations are plotted as full triangles [START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF], stars (Caesar et al. 2005) or empty squares [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF] and simulations for the 20 th century and scenarios commit, B1, A1B and A2 are represented as full grey circles (CM3) and brown full squares (MC2). [START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF], stars (Caesar et al. 2005) or empty squares [START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF] and simulations for the 2O th century and scenarios commit, B1, A1B and A2 are represented as full grey circles (CM3) and brown full squares (MC2).

List of Figures

Figure 1 :

 1 Figure 1: Difference in the average number of annual frost days between 1970-99 and 2070-99

Figure 2 :

 2 Figure 2: Same as figure 5 for maximum number of summer heat wave days. Limits of

Figure 3 :

 3 Figure 3: Same as figure 5 for number of winter days with precipitation exceeding 10 mm.

Figure 4 :

 4 Figure 4: Same as figure 5 for maximum number of summer consecutive days with precipitation

Figure 5 :

 5 Figure 5: Evolution of annual number of frost days for Alaska (top left), Canada (top right), USA

Figure 6 :

 6 Figure 6: Same as figure 5, but for maximum number of summer heat wave days.

Figure 7 :

 7 Figure 7: Same as figure 5, but for number of winter days with precipitation exceeding 10 mm.

Figure 8 :

 8 Figure 8: Same as figure 5, but for maximum number of summer consecutive days with

Figure 9 :

 9 Figure 9: Evolution of maximum number of summer consecutive days with precipitation less than 1

Figure 10 :

 10 Figure 10: Sensitivity of annual number of frost days to mean annual temperature for Alaska (top

Figure 11 :

 11 Figure 11: Same as figure 11 for maximum number of summer heat wave days.

Figure 12 :

 12 Figure 12: Same as figure 10 for 90 th percentile of T x over Europe (top) and the Mediterranean

Figure 13 :

 13 Figure 13: Same as figure 6 for maximum number of summer heat wave days calculated from

Figure 14 :

 14 Figure 14: Same as figure 9 for number of winter days with heavy precipitation (exceeding 10 mm).

Figure 15 :

 15 Figure 15: Same as figure 9 for maximum number of summer consecutive dry days (with

Figure 1 :

 1 Figure1: Difference in the average number of annual frost days between 1970-99 and 2070-99 periods, for CM3 (top) and MC2 (bottom) in the A2 scenario. Gridpoints for which the difference is non significant at the 80% level are shaded in grey. Limits of Alaska and Europe (top) and Canada (bottom) domains have been reported.

Figure 2 :

 2 Figure 2: Same as figure 1 for maximum number of summer heat wave days. Limits of Mediterranean domain (top) has been reported.

Figure 3 :

 3 Figure 3: Same as figure 1 for number of winter days with precipitation exceeding 10 mm. Limits of Canada, Usa and Europe domains (top) have been reported.

Figure 4 :

 4 Figure 4: Same as figure 1 for maximum number of summer consecutive days with precipitation less than 1 mm. Limits of USA and Mediterranean domains (top) have been reported.

Figure 5 :

 5 Figure 5: Evolution of annual number of frost days for Alaska (top left), Canada (top right), USA (middle left), Europe (bottom left) and Mediterranean countries (bottom right). Horizontal axis represents the years 1860 to 2100. Vertical axis represents the number of days. Observations are plotted as full triangles[START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF], stars(Caesar et al. 2005) or empty squares[START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF] and lines are for CM3 (dashed) and MC2 (dotted) 20 th century+A2 scenario simulations.

Figure 6 :

 6 Figure 6: Same as figure 5 for maximum number of summer heat wave days.

Figure 7 :

 7 Figure 7: Same as figure 5 for number of winter days with precipitation exceeding 10 mm.

Figure 8 :Figure 9 :

 89 Figure 8: Same as figure 5 for maximum number of summer consecutive dry days.

Figure 10 :

 10 Figure 10: Sensitivity of annual number of frost days to mean annual temperature for Alaska (top left), Canada (top right), USA (middle left), Europe (bottom left) and Mediterranean countries (bottom right). Horizontal axis represents the mean annual temperature in o C. Vertical axis represents the number of days. Observations are plotted as full triangles[START_REF] Eischeid | Creating a serially complete, national daily time series of temperature and precipitation for the western Unites States[END_REF], stars(Caesar et al. 2005) or empty squares[START_REF] New | Representing twentieth-century space-time climate variability. Part II: development of 1901-96 monthly grids of terrestrial surface climate[END_REF] and simulations for the 2O th century and scenarios commit, B1, A1B and A2 are represented as full grey circles (CM3) and brown full squares (MC2).

Figure 11 :

 11 Figure 11: Same as figure 10 for maximum number of summer heat wave days.

Figure 12 :

 12 Figure 12: Same as figure 10 for 90 th percentile of T x over Europe (top) and Mediterranean periphery (bottom).

Figure 13 :

 13 Figure 13: Same as figure 6 for maximum number of summer heat wave days calculated from yearly moving normals.

Figure 14 :

 14 Figure 14: Same as figure 10 for number of winter days with precipitation exceeding 10 mm.

Figure 15 :

 15 Figure 15: Same as figure 10 for maximum number of summer consecutive dry days.

Acknowledgments

Sources of observations were kindly provided by Alexander Gershunov, for the North American dataset and John Caesar for the recently achieved HadGHCND dataset from Met Office. A special thank should be addressed to David Salas y Mélia and Sophie Tyteca for the performance of the CNRM simulations and Jean-Louis Dufresne for the IPSL ones. This work has been undertaken in the frame of the French ESCRIME project, supported by PNEDC (Programme National d'Etude de la Dynamique du Climat) and GICC (Gestion et Impacts du Changement Climatique), and coordinated by Laurent Terray from CERFACS.