Luc André
email: luc.andre@loria.fr

Claudia-Lavinia Ignat

Gérald Oster
email: gerald.oster@loria.fr

Collaboration over Wiki Content

Keywords: ACM Classification I.7.1 Document and Text Processing: Document and Text Editing, C.2.4 Computer-Communication Networks: Distributed Systems-Distributed applications, H.5.3 Information Interfaces and Presentation: Group and Organization Interfaces-Collaborative computing, theory and models Algorithms, Design, Human Factors Real-time editing, Wiki, Collaboration, CSCW

Resolving conflicts is a key issue in collaborative editing. The difficulty of this task grows with the complexity of the document structure, and most of digital documents are not simple sequences of characters. This paper offers a new approach to handle conflict resolution automatically in a rich text document. This work uses Operational Transformation approach, and is based on a meaningful set of operations instead of primitive ones. This way, information about what the users precisely want to do is saved, and conflict resolution is more accurate.

INTRODUCTION

The Web2.0 era is associated with the growing success of participatory collaborative tools for public users. Enterprises have integrated a part of these tools in their information systems to improve their productivity and to facilitate the emergence of a form of collective intelligence. Among these tools, wikis are a good way to efficiently share a large amount of knowledge. Wikis are interlinked pages of rich text, which can be viewed and edited by every user. For instance, in a software development process, a wiki page can be dedicated to meetings, another to bug reports and a last to development progress. This way, everybody can keep an eye on when is the next meeting, who will attend, the minute of a previous meeting, what are the bugs found or fixed, and what work has been done on the project. But also edit the content without any restriction, thus allowing fast updates (wiki means fast indeed). All of this with a single tool -a wiki.

However, merging of parallel modifications on the same page is not automatically performed in most existing wiki systems such as Wikipedia. If two users are concurrently editing the same article, when they try to save their changes, the save of only one user succeeds and the other saves fail. The changes of the user whose save succeeds are published. The other users will be presented with two versions of the wiki page: the one that the user tried to publish and the last published version. Conflicts, i.e. concurrent changes on the same article, have to be manually resolved by users by re-typing or copying and pasting the changes they performed in the last version that was published. Moreover, users are not aware of other concurrent updates on the same article until they try to publish their own changes. The process of resolving conflicts might become very tedious and this can be critical when a deadline approaches and the document must be finalised.

A solution to this issue would be the real-time collaboration over wikis. Rather than requiring that users check periodically for updates, real-time collaboration is based on the principle of pushing modifications to users as soon as they are available. That is, updates are not submitted at the end of the edit on a wiki page, but each update is immediately sent at its generation, and integrated at its reception. Realtime collaboration is useful for brainstorming sessions, taking live meeting minutes, live discussion on a bug report or when editing an article when a deadline approaches.

Operational transformation approach [START_REF] Ellis | Concurrency Control in Groupware Systems[END_REF][START_REF] Sun | Achieving Convergence, Causality Preservation, and Intention Preservation in Real-Time Cooperative Editing Systems[END_REF] has been identified as an appropriate approach to be used in real-time collaborative editing to maintain consistency of the copies of shared documents. In this approach local operations are executed immediately after they are generated and remote operations are transformed against the other operations. The transformations should be performed in such a manner that the intentions of the users are preserved and, at the end, the copies of the documents converge.

Wikis can be edited either as plain text documents with a special markup-based syntax or using a WYSIWIG (What You See Is What You Get) editor which allows content (text and graphics) of the wiki page to be displayed onscreen dur-1 ing editing in a form closely corresponding to the end result.

Regarding real-time collaborative editing for the first solution, any operational transformation approach with a set of transformations designed for plain text documents [START_REF] Imine | Proving Correctness of Transformation Functions in Real-Time Groupware[END_REF] could be applied. However, applying these algorithms for wikis cannot ensure that the special syntax will be preserved after integration of concurrent operations. This might also break the underlying hierarchical structure of the wiki.

Existing software such as GoogleDocs or CoWord [START_REF] Xia | Leveraging single-user applications for multi-user collaboration: the coword approach[END_REF] are WYSIWYG editors but they do not take advantage of the underlying structure of the document. Basically they see the document as a linear sequence of elements and high level operations are translated into primitive insert, delete and update operations on basic elements. This approach leads to simple algorithms, but semantics of user operations are lost. For instance, moving a block of text is obtained by deleting the block character by character followed by re-inserting each character of the block. If a user performs some modifications into a block of text that is concurrently moved, then these user changes are either completely lost or they are placed outside the context of the moved block of text. In this case user intention of modifying the paragraph is lost.

In this paper, we propose to use a traditional operational transformation approach for which we define operations with high-level semantic capturing user intentions when editing wiki content. We provide the required set of transformations for these operations. This paper is organised as follows. First section presents existing approaches offering support to real-time collaboration over rich text documents. Second section presents our approach: our document model, our operations and the associated transformations. Third section discusses the benefits and the limitations of managing operations which captures high-level user intentions. Fourth presents our on-going validation in the context of the XWiki 1 system. Finally, last section concludes and presents our directions of future work.

RELATED WORK

CoWord [START_REF] Xia | Leveraging single-user applications for multi-user collaboration: the coword approach[END_REF] is a plug-in for Word using a strategy called Transparent Adaptation (TA), with Operational Transformation (OT) collaboration supporting technique. Basically, OT technique sends operations to other users when they are locally generated, and transforms received operations so they can be executed on a different state (than the state of the generation). TA technique converts every high-level operation to a sequence of primitive operations. OT technique is applied to this sequence of primitive operations. So TA is application-dependant, but not OT operations, allowing easy software updates : one just needs to turn new high-level operations into primitive ones. In CoWord, the set of primitive operations is Insert, Delete and Update. It is enough to create any Word (rich text) document, but the transformation of high-level operations into these ones erases all information about the original high-level operation. For instance, moving a character is transformed into one Delete operation 1 http://www.xwiki.com/ followed by one Insert. Concurrently moving a sequence of ten characters while inserting a new character between the fourth and the fifth one will result in the ten characters moved (deleted then inserted), and the new single character inserted outside of its context. The expected result is to have the new character between the others, as the user intended to. Information about the move intention is discarded. GoogleDocs2 and Etherpad3 work in a similar way. All edits are transformed into three basic types of changes: inserting text, deleting a range of text and applying styles to a range of text. Transformations are provided for all pairs of these types of changes. However, these operations are not enough for capturing user intention. For instance, the previous provided scenario leads to the deletion of the moved sequence of characters together with the new inserted character and the re-insertion of moved sequence of characters at the new position. The new inserted character disappears. Docx2Go [START_REF] Puttaswamy | Docx2go: collaborative editing of fidelity reduced documents on mobile devices[END_REF] is a framework for collaborative editing over XML documents on mobile devices where not all devices have the complete document. It adapts the Logoot [START_REF] Weiss | Logoot: A scalable optimistic replication algorithm for collaborative editing on p2p networks[END_REF] approach for XML documents. XML elements possess unique identifiers, the set of identifiers being ordered and dense. Docx2Go supports four types of operations at the element level: insert adds a new element at a specific location in the relative order; delete removes a specified element; update changes the internal contents of an element; and move changes the relative order of a specified element with respect to other elements. When one element is concurrently edited, the generated conflict can be resolved manually or automatically. In the case of a manual resolution the owner of the document is in charge of resolving the conflict. However, very often in collaborative editing multiple users edit the document and there is no explicit owner of the document. In the case of automatic resolution, when concurrent updates are performed on the same element, the element will be duplicated, each version of the element including the individual changes performed. However, if the element is a paragraph, the user will be provided with as many versions of the paragraph as the number of concurrent changes. The paper presents no awareness mechanism that would inform users about the different versions of the elements that were concurrently changed.

As we can see, there is no suitable mechanism that offers an automatic resolution of conflicts that reflects closely user intentions. We claim that an approach that preserves user intentions should contain a rich set of operations for which intentions are precisely specified. Combined effects of pairs of these operations have to be provided.

APPROACH System architecture

Figure 1 gives an overview of the architecture of the wiki system. It consists of a wiki server that stores all wiki pages and a set of clients. Each time a user wants to edit a wiki As soon as a client performs a change on his replica, this change is sent to the server that processes it by potentially performing some transformations and then sends it to the clients which at their turn might transform it before execution.

The proposed operational transformation approach is composed of an integration algorithm and a set of transformation functions. Any integration algorithm such as Jupiter [START_REF] Nichols | High-latency, Low-bandwidth Windowing in the Jupiter Collaboration System[END_REF], COT [START_REF] Sun | Context-based Operational Transformation in Distributed Collaborative Editing Systems[END_REF] or SOCT4 [START_REF] Vidot | Copies Convergence in a Distributed Real-Time Collaborative Environment[END_REF] can be used. In our implementation we used Jupiter algorithm. Transformation functions for the defined set of operations are proposed in the appendix of this paper and briefly described in the next subsections.

Document model and operations

Our approach uses one operation for one intention. To fully express the hierarchical organisation of the document, it is represented as a tree. The root is a "document" node, the level below is "paragraph" nodes, and then is the content. Content nodes are either text nodes, or style node with a unique child -a text node -and attributes representing the styles. Figure 2 gives an illustration of our document model. • move one paragraph moveP(int startposition, int endposition) startposition : index of the paragraph to be moved in the document endposition : index where the paragraph is moved • delete a subtree (keeping a tombstone) deleteTree(int[] path) path : path to the node to be deleted Parameters presented in italic are not required to execute the operation, but they refer to required information for transformations. These parameters are updated during transformations. The document illustrated in Figure 2 can be created by executing the following operations: user1 creates a new paragraph, inserts "abcdef", applies bold style to "cd", while user2 creates another paragraph and inserts "ghijkl", and while user3 creates another paragraph, inserts "mnopq" and applies italic style to "'mn".

document ff ff ff ff ff Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z p k k k k k k k S S
We intend to extend these operations to handle headings, lists, tables, links and images. We do not need to create one new operation for every new intention. For instance, headings can be managed like paragraphs, but with "h1" nodes instead of "p" nodes. Links can be stored in a "style" node, with "link" as parameter, and "http://...." as value. However, this will require to update the presented transformation functions.

Overview of the proposed transformation functions

As we have eight operations, we must define sixty four transformations. Due to space limitation, we only provide a brief overview of our transformations. Interested reader can refer to the appendix for the full set of transformation functions.

When a newP operation is transformed, the insertion position is updated if some paragraphs were concurrently moved, merged, split or inserted. The parameter "id" is used to break some ties. The tricky case occurs when the new paragraph is inserted between two concurrently merged paragraphs. In this case it is appended after the merged paragraphs.

mergeP operations are transformed according to the same principles. However they are more tricky cases to deal with. If one paragraph was inserted between the merged ones, we need to first move the inserted one, then to merge the two other paragraphs. And if one of the merged was concurrently moved, we need to move the second before merging. leftchildren and rightchildren parameters respectively store the number of children of the left and the right paragraphs before the merge occurs. It is useful for instance to know in which child we have to insert a character in the case of a concurrent insertion.

splitP is more complex to handle, since it needs a whole path (not just a paragraph position) and a character position. The more difficult cases are those which involve an operation that modifies path and position. For instance, starting from document illustrated in Figure 2, transformation of splitP(2, 1/0) -split after "h" -with textStyle(1, 4, 1/0, underlined, true) -underline "hij" -leads to splitP(1, 1/1/0). For the sake of clarity, parameters presented in italic were omitted.

moveP operation works in the same way as newP and mergeP operations -with paragraph positions -. The tricky case appears when merge or move involving the same paragraphs concurrently occurred with a moveP operation. In such a case, the tie is broken using the end position parameter.

insertText operation is close to splitP operation, as it carries a position and a path parameters, but does not change the structure of the tree. To transform an insertion operation, the new path is computed according to concurrent newP, mergeP, splitP, moveP, textStyle operations and the new position is computed regarding concurrent splitP, insertText, deleteText, textStyle operations. The same principle is applied for deleteText operation except that a tie breaker parameter is no needed "id", since two concurrent deletions of the same characters never conflict: the character is deleted anyway.

textStyle is the most complex operation to manage. It carries a path, two character positions, and can split a node into three others, while adding a child to one of them. For the sake of simplicity we only explain how transformation is performed when two concurrent textStyle operations occur. If they do not target the same paragraph, no transformation is performed. Else, if they do not target the same child, the path of the second textStyle operation has to be updated if the first one split its child into two or three children. Else,they target the same child -, in this case, the two operations may overlap, so the transformation of one textStyle operation may result into two or three textStyle operations. It has also to check if the two styles are compatibles. If they are not, "id" is used as the tie breaker, but the discarded style is still applied (with the winner one as parameter) to apply the structure modifications. Other parameters -presented in italic -are, "addStyle" to store that a "style" node was created, "splitleft" to store that there were some characters in the child before "start" index, and "splitright" after "end" index. A generated textStyle(1,4...) indeed creates a node at the left of the child, while textStyle(0,3...) does not. So if a concurrent deleteText(0,...) turns textStyle (1,4...) into textStyle(0,3...) without any information, documents may diverge.

deleteTree operation is a tombstone-based deletion and is easy to transform -only path has to be updated -. However, it implies to write carefully some operations. For instance, if two paragraphs are merged while one is deleted, the expected result is to have the children of the deleted paragraph invisible, and the others visible. In this case the merge operation is not transformed, and the operation itself checks if the paragraph is a tombstone, and turns its children into tombstone too if needed, then move them for the merge. And the deleteTree operation is turned into as many deleteTree as the deleted paragraph has children. That is one reason why we need to store "leftchildren" and "rightchildren" as mergeP parameters.

DISCUSSIONS

Our approach captures user intentions into the design of the set of operations. However, the number of operations is higher than in other existing approaches and therefore transformations are multiple and complex.

One can claim that chances that users edit at the same time the same part of a document leading to conflicts are not very high. Even if conflicts occur in the real-time collaboration their automatic resolution can be quickly noticed and an undesired resolution effect can be manually repaired.

But in an asynchronous collaboration where users can perform changes on their local copies of the document and then publish them at a later time conflicting situations become more critical. In this collaboration mode users are not informed about concurrent changes of other users. When users publish their changes and have to merge them with concurrent changes performed by other users a lot of conflicts might have to be resolved. A manual conflict resolution mechanism might be very tedious for a user. An automatic resolution mechanism must take into account user intentions because otherwise a non meaningful result might be obtained. It is in this asynchronous collaboration that our approach offers a powerful solution compared to existing approaches based on primitive operations. Consider the simple case when a user moves some text and keeps editing it, while another user moves it elsewhere and edits it as well. In most existing approaches the final result will be two modified pieces of duplicated text. These pieces of text are meant to be manually merged, so users have to notice it and to properly merge them. Our approach prevents this situation as it captures the semantics of move and modify operations. In this simple example no duplication is performed.

EVALUATION

Correctness of transformation functions

The transformation functions have to satisfy condition C 1 [START_REF] Suleiman | Concurrent operations in a distributed and mobile collaborative environment[END_REF]. Being given two concurrent operations op 1 and op 2 , the relation op 1 • T (op 2 , op 1 ) ≡ op 2 • T (op 1 , op 2 ) must hold. The notation op 1 • op 2 denotes the sequence of operations containing op 1 followed by op 2 . This property expresses an equivalence between two sequences of operations, i.e. when the sequences of operations op 1 followed by T (op 2 , op 1 ) and op 2 followed by T (op 1 , op 2 ) are applied on the same initial document state, the same document state is produced.

We have designed our transformation functions in order to respect C 1 condition. We are working on formally proving that C 1 is respected by using SPIKE theorem prover.

Implementation

We are currently integrating our approach in the XWiki system. XWiki is a java-based wiki that runs on a servlet container such as Tomcat or Jetty. The Jupiter approach required that the same algorithm is running on the server side and on the client side. In our implementation, the client side algorithm code is exactly the same as the server side algorithm code except that it is compiled using the GWT 4 from Java to Javascript. 4 Google Web Toolkit http://http://code.google.com/webtoolkit/

We propose to show a demonstration of our wiki extended for real-time collaboration during the workshop.

CONCLUSION AND FUTURE WORK

This paper presented a new approach to create operations for OT technique in the field of collaborative editing. This approach is based on high level operations instead of primitive operations, and is designed to capture user intentions. We now have to enlarge our set of operations and to prove the correctness of our transformations.Then our next investigation will be to do real case studies to measure if the added value is worth the cost -in operations and transformationsof this approach.

Figure 1 .

 1 Figure 1. Architecture of the wiki system

Figure 2 .

 2 Figure 2. Document model. On this document hierarchical model, we define the following operations: • create a new paragraph with an empty text node. newP(int position, int id) position : index of the paragraph in the document id : unique site identifier that generated the paragraph • merge two adjacent paragraphs (the children of the right paragraph are appended to the left one) mergeP(int position, int leftchildren, int rightchildren) position : index of the left paragraph in the document

https://docs.google.com/

http://etherpad.com/

APPENDIX

Utility functions


Frédéric Lefèvre
email: frederic.lefevre@insa-lyon.fr

Jean-Baptiste Conrardy

Martin Raynaud

Jocelyn Bonjour

Experimental investigations of flat plate heat pipes with screen meshes or grooves covered with screen meshes as capillary structure

Keywords: flat plate heat pipe, screen mesh layers, grooves, experimental study, electronic cooling

Experimental investigations of two different flat plate heat pipes (FPHP) are presented. The capillary structure is made of one or two screen mesh layers for the first FPHP and screen mesh covered grooves for the second FPHP. The heat pipes, filled with methanol, were tested in different configurations i.e. with various locations of heat sinks and heat sources, numbers and natures of the heat sinks and orientation. Water heat exchangers were first used as heat sinks to estimate the performance of the capillary structures. Experiments were also performed with aluminium radiator cooled by natural convection of air in order to show the performance of the FPHP in experimental conditions representing a practical case, typically the cooling of electronic equipments. The results show the interest of this solution for the proposed application. The method chosen to assemble this FPHP prototype with meshes is very simple and cheap. On the contrary, the performance of the heat pipe obtained with the association of grooves and meshes is not as high as one could expect. Indeed, if this capillary structure allows working in tilted unfavourable position, which is not possible with grooved heat pipe, a clear nucleate boiling limitation is observed for rather small heat fluxes.

Introduction

The interest in the use of heat pipes for thermal management is recognized in many industrial applications. For example the thermal management of electronic equipments has become an important issue because of increasing power levels along with the miniaturization of the devices.

With the advent of denser device packaging and faster intrinsic speeds, cost, reliability and size have been improved, but it requires new cooling solutions often based on liquid/vapor phase change systems. As a first approach, the thermal performance of a heat pipe can be characterized by both its overall thermal resistance and its maximum power in horizontal and vertical positions. These characteristics depend mainly on the capillary structure, which is usually made of grooves, meshes, sintered powder or a combination of them. In many applications, heat pipes are circular and are used to transport heat from one heat source to one heat sink, which can be any cooling system.

Planar heat pipes, also called flat plate heat pipes have the same components, but offer a wide cross-section, which allows reducing their thickness without reducing their thermal performance.

Furthermore, several heat sources can be located on them, which is interesting to cool electronic cards, with many electronic components.

Lots of experimental and theoretical works have been published on flat plate heat pipes with rectangular grooves or also on micro heat pipes arrays in both steady [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF][START_REF] Lefèvre | Prediction of the temperature field in flat plate heat pipes with micro-grooves -Experimental validation[END_REF][START_REF] Longtin | A one-dimensional model of a micro heat pipe during steady-state operation[END_REF][START_REF] Launay | Investigation of a wire plate micro heat pipe array[END_REF][START_REF] Wang | Analysis of wire-bonded micro heat pipe arrays[END_REF] and transient states [START_REF] Sonan | Transient thermal and hydrodynamic model of flat heat pipe for the cooling of automotive electronic components[END_REF][START_REF] Harmand | Transient cooling of electronic components by flat heat pipes[END_REF].

Numerical models of such capillary structures are generally based on conservation equations and on Young-Laplace's law, which links the shape of the liquid-vapour interface to the hydrodynamic parameters [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF][START_REF] Lefèvre | Prediction of the temperature field in flat plate heat pipes with micro-grooves -Experimental validation[END_REF][START_REF] Longtin | A one-dimensional model of a micro heat pipe during steady-state operation[END_REF][START_REF] Launay | Investigation of a wire plate micro heat pipe array[END_REF][START_REF] Wang | Analysis of wire-bonded micro heat pipe arrays[END_REF]. Thus, the shape of the liquid-vapour interface is calculated at each point of the grooves. In addition, recent experimental works presented accurate measurements of the meniscus in grooved FPHP using confocal microscopy [START_REF] Lefevre | Confocal microscopy applied to capillary film measurements in a radial flat plate heat pipe made of silicon[END_REF][START_REF] Lips | Combined effects of the filling ratio and the vapour space thickness on the performance of a flat plate heat pipe[END_REF][START_REF] Lips | investigation of evaporation and condensation processes specific to grooved flat heat pipes[END_REF]. Thus, numerical models can be validated and a detailed description of the physical mechanisms involved in a grooved heat pipe is now available.

In [START_REF] Lips | Nucleate boiling in a flat grooved heat pipe[END_REF], nucleate boiling was observed at the evaporator of a grooved FPHP for relatively small heat fluxes (~ 3 W/cm²). The authors showed that the phenomenon of nucleate boiling improves the thermal performance of the flat heat pipe, and they emphasized that the presence of bubbles does not prevent the proper circulation of the fluid, contrary to what is generally stated in the literature and referred to as "boiling limit". Dryout of the evaporator was observed for heat fluxes much higher than the heat flux of onset of nucleate boiling. In [START_REF] Lips | Physical mechanisms involved in grooved flat heat pipes: experimental and numerical analyses[END_REF], Lips et al. showed, using confocal microscopy measurements that this dryout was not due to the boiling phenomenon but that it was a classical capillary limit.

In more complex capillary structures such as meshes or sintered powder, it is difficult to calculate the exact location of both the liquid and the vapour inside the system and also difficult to determine it experimentally. Theoretical model are based on Darcy's law, with the permeability and the equivalent thermal conductivity of the capillary structure as main parameters. Experimentally, temperature measurements are used to estimate the maximum power and the overall thermal resistance. In addition, some papers present transparent heat pipes to visualize phenomena occurring in working conditions. Nevertheless, a fine description of the liquid-vapour interface is not yet available.

Kempers et al. [START_REF] Kempers | Effect of number of mesh layers and fluid loading on the performance of screen mesh wicked heat pipes[END_REF] tested the effect of the number of screen mesh layers (wire diameter 109 µm) and fluid filling on a circular heat pipe of length 177.8 mm and inner diameter 6.22 mm. As expected, the maximum heat transfer increases with the number of meshes, but the increase in thermal resistance due to the increase of mesh number is found to be significantly lower than that predicted by conduction-based models. These authors showed that decreasing the amount of working fluid decreases the effective thermal conductivity but also the maximum power. In another study [START_REF] Kempers | Characterization of evaporator and condenser thermal resistances of a screen mesh wicked heat pipe[END_REF], Kempers et al. showed that heat transfer in the condenser is reasonably equal to that calculated by conduction models, while at the evaporator, a threshold due to nucleate boiling changes significantly heat transfer coefficients. The work of Kempers et al. [START_REF] Kempers | Characterization of evaporator and condenser thermal resistances of a screen mesh wicked heat pipe[END_REF] confirms observations made by Lips et al. [START_REF] Lips | Nucleate boiling in a flat grooved heat pipe[END_REF] in grooved capillary structures: boiling activity in the screen wick was in fact observed to augment performance, not to limit it.

Wong et al. [START_REF] Wong | Visualization and performance measurement of operating meshwicked heat pipes[END_REF] made visualisations of the evaporation/boiling process in transparent circular heat pipes of length 150 mm and inner diameter 5 mm. Two layers of screen mesh are placed in the pipe.

Two different meshes were tested (wire diameters 114 µm and wire diameters 55 µm). They observed nucleate boiling for heat fluxes higher than 15 W/cm² at the evaporator. In two other articles, Wong et al. [START_REF] Wong | Evaporation resistance measurement with visualisation for sintered copper powder evaporator in operating flate plate heat pipes[END_REF] and Liou et al. [START_REF] Liou | Visualisation and thermal resistance measurement for the sintered mesh-wick evaporator in operating flat plate heat pipes[END_REF] reported visualisations in transparent flat plate heat pipes, made of sintered screen meshes (same characteristics as in [START_REF] Wong | Visualization and performance measurement of operating meshwicked heat pipes[END_REF]) or sintered copper powder.

In both works, they did not observe nucleate boiling even for high heat fluxes (60 W/cm²). In these three works [START_REF] Wong | Visualization and performance measurement of operating meshwicked heat pipes[END_REF][START_REF] Wong | Evaporation resistance measurement with visualisation for sintered copper powder evaporator in operating flate plate heat pipes[END_REF][START_REF] Liou | Visualisation and thermal resistance measurement for the sintered mesh-wick evaporator in operating flat plate heat pipes[END_REF], observations of wetted area or nucleation process were made by a CCD camera. Obviously, this technique does not permit to measure the exact location of the liquidvapour interface but provides some useful qualitative information.

Li et al. [START_REF] Li | Evaporation/Boiling in thin capillary wicks (I) -Wick thickness effects[END_REF][START_REF] Li | Evaporation/Boiling in thin capillary wicks (II) -Effects of volumetric porosity and mesh size[END_REF] studied the evaporation/boiling phenomena inside sintered screen meshes (wire diameters 56 µm, 114 µm and 191 µm). Experimental results showed that while the evaporation/boiling heat transfer coefficient is not affected by the thickness of the capillary structure, the critical heat flux increases proportionally to this thickness. Furthermore, the evaporation/boiling heat transfer coefficient decreases with the wire diameter, but is not strongly dependant on the porosity. On the contrary, the authors showed that the critical heat flux increases with both the wire diameter and the porosity. In [START_REF] Li | The effective thermal conductivity of wire screen[END_REF], Li et al. presented a detailed and comprehensive literature review on the effective thermal conductivity of screen meshes. They also developed an analytical model, in which the number of meshes, the wire diameter and the compression factor are preponderant. The model was compared to experimental data. Do et al. [START_REF] Do | Thermal resistance of screen mesh wick heat pipes using the water-based Al 2 O 3 nanofluids[END_REF] investigated the thermal performance of screen mesh wick heat pipes using waterbased Al 2 O 3 nanofluids. A significant decrease of the thermal resistance was observed. The authors showed that this enhancement of the thermal performance is due to the thin porous coating layer formed by nanoparticules at the wick structure, a phenomenon that was described in details for pool boiling experiments by Stutz et al. [START_REF] Stutz | Influence of nanoparticle surface coating on pool boiling[END_REF]. This article reports experiments performed with two flat plate heat pipes with rather large dimensions. These heat pipes essentially differ from their capillary structure, which is made of screen meshes for the first FPHP and of screen meshes associated with rectangular grooves for the second FPHP. The meshes are not sintered like in [START_REF] Li | Evaporation/Boiling in thin capillary wicks (I) -Wick thickness effects[END_REF][START_REF] Li | Evaporation/Boiling in thin capillary wicks (II) -Effects of volumetric porosity and mesh size[END_REF], but plated against the wall by means of a coarse screen mesh, as recommended in [START_REF] Rosenfeld | Flexible heat pipe[END_REF]. This technological solution makes it very easy to assemble. The heat pipes have been tested in different configurations, i.e. one or two layers of mesh were used, several locations of the heat sink(s) and heat source were tested with various numbers and natures of the heat sinks and for different orientations.

Experimental set-up

FPHP made of one or two screen mesh layers

The first flat plate heat pipe under investigation (called heat pipe n°1 in the following) is shown in figure 1. It is made of one copper plate of thickness 1.5 mm and surface 267115 mm². The FPHP is hermetically sealed on its upper face with a transparent plate, which allows observations inside the system. A Viton flat ring of thickness 2 mm is placed between the copper and the transparent plates to ensure tightness. The capillary structure, of dimensions 230  90 mm 2 , is made of 1 or 2 CuSn 325 square screen mesh layers (figure 2). The capillary screen meshes are plated against the copper plate by means of a coarse screen mesh, which creates the vapor space. Eight micro grooves are etched at the back of the copper plate in order to embed 100 µm diameter thermocouples (uncertainty lower than 0.2 K), using silver lacquer in order to reduce the contact resistance (figure 1). Their voltage is recorded by a Keithley 2700 multimeter.

The heat source is a thick resistor film of dimensions 55.196.5 mm 2 and resistance 90.6 , which is supplied by a stabilised DC power supply. It is plated against the copper wall by means of high conductive thermal grease. Electric power is obtained by measuring the voltage drop across the heating resistor and the intensity, by means of a calibrated resistance. Thus, the uncertainty for the heating power is negligible. Two different heat sinks are tested:  Two aluminium radiators (140170 mm 2 ) cooled by natural convection of air at ambient temperature. Two thermal wedge locks are screwed on each radiator to maintain the FPHP by means of two small fins located on each side of the FPHP (figure 1). The contact area between the thermal wedge lock and the heat pipe is equal to twice 105  5 mm². These radiators are used to simulate a practical application, namely the cooling of electronic cards, which are most of the time located inside a metallic rack. The rack is used as a radiator to dissipate heat to the ambient air. The idea is to insert the FPHP into the metallic box exactly like an electronic card, using thermal wedge locks.

 One or two water heat exchangers of heat transfer area 30 × 90 mm 2 . The water flow rate is constant and the inlet temperature is controlled by means of a thermostatic bath in order to have a constant temperature for all experiments. It is useful for the determination of the FPHP characteristics. Heat sinks are plated against the copper wall using high conductive thermal grease.

FPHP made of grooves covered by two screen mesh layers

The second FPHP under investigation (figure 3, heat pipe n°2) is made of 109 longitudinal microgrooves, covered by two screen mesh layers. The grooves are machined in a copper plate. They are similar to those of another FPHP already described in previous articles [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF][START_REF] Lefèvre | Prediction of the temperature field in flat plate heat pipes with micro-grooves -Experimental validation[END_REF]. Each groove has a rectangular cross-section of height and width equals to 380 µm and 400 µm, respectively. The distance between two grooves is equal to 400 µm. The area of the grooved surface is equal to 230  90 mm 2 . The vapour space, machined inside the copper plate, has a height of 1.6 mm. The wall thickness under the grooves is equal to 2 mm. The FPHP is hermetically sealed on its upper face with a transparent plate and a Nitril o-ring to ensure tightness. If good thermal performance was obtained with this heat pipe in horizontal position (or even in vertical favourable position) [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF][START_REF] Lefèvre | Prediction of the temperature field in flat plate heat pipes with micro-grooves -Experimental validation[END_REF], it was not able to work in tilted position because capillary pressure induced by the grooved capillary structure was too small to overcome hydrostatic pressure drop in vertical position. This justifies the adjunction of the two layers of screen mesh to the original groove FPHP: in order to overcome this limit, these screen meshes were plated against the grooves, similarly to the method used in section 2.1, in order to increase the capillary pressure gradient while preserving the high permeability of the grooves. The heat source is plated on the copper wall. It is a thick resistor film of area 190 × 90 mm 2 . This resistor of 2.1  is supplied by a DC power supply. The heat sink is a water heat exchanger whose characteristics are the same as the heat exchangers presented in section 2.1. The heat source and the heat sink are separated by an adiabatic area of length equal to 10 mm. They are both plated against the copper wall using high conductive thermal grease. It has to be noted that the heat source area is much larger than those of the heat sink and of the adiabatic surface. The reason is the initial foreseen application of that FPHP that was the cooling of proton exchange membrane fuel cells.

The same characteristics have been retained for this study to allow comparison with previous results [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF]. Seven thermistors (uncertainty lower than 0.2 K) are located along the wall and the value of their resistance is recorded by a Keithley 2700 multimeter.

Experimental results

Both FPHPs are thermally insulated during thermal tests with 5 cm thick fiberglass insulation. As a result, considering a heat transfer coefficient of 10 W/m²K between the fiberglass insulation and the ambient air and a maximum temperature difference of 40 K between the heater and the ambient air, the heat losses over the heater are lower than 0.5 W for the FPHP n°1 and lower than 0.15 W for the FPHP n°2.

Both FPHP are first degassed and filled. In order to promote surface wetting, the copper plate is first cleaned. The FPHP and the working fluid are degassed carefully to eliminate the noncondensable gases. The method of evacuating the non-condensable gases from the working fluid is based on the fluid solidification under vacuum. The fluid contained in a heated vessel vaporizes, releases non-condensable gases and solidifies in a second vessel immersed into liquid nitrogen. The non-condensable gases are evacuated by vacuum pumps. The FPHP is degassed by heating during vacuum pumping at 10 -5 mbar.

FPHP made of one or two screen mesh layers

The heat pipe n°1, filled with methanol, has been tested in different configurations. The optimal filling ratio (i.e. the filling ratio corresponding to the smallest thermal resistance of the FPHP, which is measured as the ratio of height of liquid to height of FPHP in vertical position) is around 20% when the FPHP is horizontal. It is found to be slightly lower when the heat pipe is tilted.

Experiments with one heat source and one heat sink located on both extremities of the heat pipe

In this part, the FPHP n°1 is tested with one heat source and one heat sink, each located at one extremity of the heat pipe. This is the worst configuration because liquid and vapour have to flow along the whole length of the heat pipe, which generates high pressure drops. Nevertheless, this configuration is interesting to evaluate the heat transfer capability of the heat pipe.

The working temperature is set to around 30 °C. Figure 4 symbolized by two rectangles on the x axis. A proper working of the heat pipe is observed for powers lower than 18 W. Beyond this value, a sudden dryout is observed, which degrades the thermal performance: the capillary limit is reached.

Figure 5a presents the maximal temperature difference (i.e. the difference between the maximum evaporator and minimum condenser temperatures) vs. power for the FPHP having one or two screen mesh layer(s), in horizontal orientation. In order to have a comparison criterion, the maximum temperature difference obtained by heat conduction through the copper plate that forms the body of the heat pipe only is presented. This last curve has been obtained using experimental results performed with a power of 10 W, which were linearly extrapolated for the other powers. With one or two screen meshes, the maximum temperature measured with the FPHP is much smaller than that with the copper plate of thickness 1.5 mm. The temperature field obtained for the copper plate has been compared to a heat conduction model with a thermal conductivity of copper equal to 400 Wm - 1 K -1 . The comparison shows that heat losses of the system are lower than 10 %. Figure 5b presents the same results, but the y scale is expanded 4 times. A linear behaviour is observed until a threshold power for which the maximum temperature difference increases. This threshold is relatively similar with one screen mesh (~ 18 W) and 2 screen mesh layers (~ 22 W).

However the transition is abrupt with one mesh, whereas it is smoother with two meshes. For the case with one mesh, the threshold undoubtedly corresponds to the capillary limit. For the 2 meshes case, a so smooth variation implies that evaporation still occurs at the evaporator. There is probably a narrow dryout between the mesh and the copper plate, but liquid is still drained to the evaporator by the meshes. Furthermore, a linear behaviour is also observed for increasing powers between 22

W and 40 W. Beyond 40 W, this linear tendency is not observed any longer. These results show that the liquid film shapes inside such a capillary structure is complex and still needs to be understood.

In the linear part of the curve, the thermal resistance of the heat pipe, defined as the maximum temperature difference divided by the power, is around 0.23 K/W for one screen mesh layer, 0.38 K/W for 2 screen mesh layers before the first threshold and 0.5 K/W beyond it. In comparison, the thermal resistance of the copper plate is equal to 2.3 K/W. In other words, a copper plate with the same thermal performance as the heat pipe with one mesh should be 15 mm thick. and 10 % (h = 2 cm) respectively. The other symbols correspond to increasing tilt angles (0°, 10°, 25 °, 35 ° and 45°), the heat source being above the heat sink. When the heat pipe is inclined, the best thermal performance is obtained for a filling ratio smaller (10 %) than in horizontal orientation (20 %), which is due to the excess of liquid at the condenser. The temperature field is rather homogeneous in the condenser and the adiabatic area, but it becomes less homogeneous at the evaporator when the tilt angle increases. However, in all the cases, temperature levels are considerably smaller than what they would be for heat conduction in a copper plate (line and star symbols). It has to be noted that experimental results in vertical position are not presented. Indeed, in all the cases, the maximum capillary pressure of the screen mesh layers is not sufficient to overcome the hydrostatic pressure.

Figure 6: Temperature profile along the heat pipe n°1 for a power of 10.2 W with a reference temperature of 0° at the condenser

Experiments with one heat source and two heat sinks

In this part, we present temperature fields measured with two heat sinks at each extremity of the heat pipe n°1. This configuration corresponds to the foreseen application. The FPHP is supposed to be inserted in a metallic rack or chassis, used as a radiator to dissipate heat from the electronic components. The metallic rack can be used in very harsh conditions (dusty environment and high temperature levels). Thus, it is not possible to cool it directly from the inside, since it has to be tightly closed in working conditions. As a result, the heat generated by electronic components has to be transported from the inner of the rack to its external surface, where it is removed by both natural convection and radiation. A conductive plate in aluminium is used for that purpose but its thickness is important. The aim of the study is thus to replace this conductive plate by a FPHP.

For the laboratory tests of the FPHP, a single heat source is located in the middle of the FPHP. In real conditions, several electronic components would be located on the FPHP. The capillary structure is made of 2 mesh screen layers.

Figure 7 presents temperature profiles in horizontal orientations with two types of heat sinks: two water heat exchangers cooled by a thermostatic bath at a temperature close to 20°C or two aluminum radiators cooled by natural convection with air at ambient temperature. The thermal load is equal to 15 W. The overall shapes of temperature fields are very similar for these two cases. The only difference is the mean temperature level, which is close to the heat sink temperature for water heat exchangers and 30°C higher for air radiators. This difference is due to the nature of the heat sinks and not to the FPHP: the thermal resistance of air radiators is much higher than that of water heat exchangers. As a consequence, the heat exchangers impose their temperature at the condenser.

However, this comparison underlines that the nature of the heat sink does not change the FPHP behaviour. The next remaining results were obtained with water heat exchangers, which were preferred for practical reasons for that experimental campaign since steady states were obtained very quickly. Of course, water heat exchangers will not be used in the foreseen application;

otherwise, the use of a heat pipe would not be necessary. Figure 8 presents the maximal temperature difference between the heat source and the heat sinks in horizontal position vs. power. For the heat pipe n°1 with two mesh screen layers, linear characteristics are obtained until a threshold power of 82 W for which the thermal resistance is equal to 0.14 K/W. A copper plate with the same thermal performance would be more than 7 mm thick and an aluminium plate ( = 160 W/mK) would be 18 mm thick, which shows the interest of using a FPHP to reduce the size and the weight of the thermal drain.

The maximum power is much higher than in the experiments presented in section 3.1.1. Indeed, for a given heat input, only half of the heat is transported to each end. Furthermore, the path followed by the liquid and the vapor inside the heat pipe n°1 is much shorter. As a matter of fact, a shorter path reduces pressure drops and thus increases the heat transfer capacity. Similarly to section 3.1.1, a linear tendency is also observed after the first threshold, which shows that evaporation still occurs at the evaporator but there exists probably a narrow dryout between the mesh and the copper plate. effects. On the contrary, on the bottom part of the FPHP, capillary pressure is not sufficient to overcome the hydrostatic pressure. Nevertheless, the heat sink located on the top of the FPHP is sufficient to cool the heat source. The minimum temperature considered for that experiment is the temperature at the condenser located on the top. This is the reason why temperatures decrease to negative values at the bottom of the pipe.

FPHP made of grooves covered by two screen mesh layers

In this part, we present results obtained with the heat pipe n°2. The capillary structure is made of 109 grooves covered by 2 screen mesh layers. The FPHP is filled with methanol. Excellent thermal performance was obtained with the same FPHP without screen mesh in horizontal position, but the FPHP was not able to work in vertical unfavourable position [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF]. The aim of these new experiments is to check the ability of a combination grooves and meshes to work in tilted position.

Figure 10 presents temperature fields measured in horizontal orientation. The FPHP has been tested by increasing gradually the power from Q = 1.9 W to Q = 72.8 W. The thermal resistance decreases slowly from 0.2 K/W to 0.04 K/W, when the power increases, until a threshold value of 70 W.

Beyond this value, a sudden dryout occurs on the whole capillary structure and the thermal resistance reaches a value of 0.24 K/W. These results must be compared to the experimental results obtained with the same FPHP without the screen meshes, presented in a previous paper [START_REF] Rullière | Prediction of the maximum heat transfer capability of two-phase heat spreaders -Experimental validation[END_REF]. For a power of 51.3 W, the thermal resistance was equal to 0.023 K/W. In the present experiment it is equal to 0.045 K/W for Q = 51.5 W. The difference is due to the additional thermal resistance of the 2 screen mesh layers. The second parameter that has to be compared is the capillary limit, which was higher than 150 W without the screen meshes. Furthermore, the dryout was not observed on the whole surface of the FPHP, but only at its extremity. In the present experiment, beyond 70 W, the entire surface is dry. This comparison shows that the limit reached in the present experiment is not a capillary limit but rather a boiling limit. This catastrophic dryout is probably due to the rapid expansion of bubbles, which grow between the screen mesh layer and the grooves, rather than outside of it, because of the capillary pressure barrier imposed by the meshes. As a result, bubble growth pushes away the liquid from the grooves. As the screen mesh layers are not able to drain the liquid on the entire surface, the capillary structure suddenly dries out after the boiling incipience.

As soon as the capillary structure is dry, a power decrease does not allow rewetting it. A strong hysteresis is observed. Furthermore, if the power does not increase progressively like in figure 10, but abruptly, dryout occurs for a much lower power than the threshold observed in figure 10. All these observations show a strong limitation of the association meshes and grooves. In horizontal position, the maximum heat flux is considerably reduced compared to that obtained with a simple grooved surface. This association allows using FPHP in tilted position, but nucleate boiling in narrow space occurs for rather small heat fluxes (~ 0.2 W/cm²). All these observations shall be investigated more accurately to understand the physical mechanisms responsible for this behaviour.

Conclusion

Experimental data obtained with two different flat plate heat pipes of similar dimensions were presented. The assembly of the first FPHP is very simple and show good thermal performance for the proposed application. FPHP thermal performance does not depend on the nature of the heat sinks: experimental results are similar using air radiators as cold sources rather than water heat exchangers. Good thermal performance is also observed in various tilted positions when two heat sinks are used at each extremity of the FPHP. In horizontal position, a clear threshold is observed with one mesh when the capillary limit is reached whereas it is less explicit with 2 meshes. The results obtained with the association of grooves and meshes are disappointing. Indeed, even though this association allows working in unfavourable tilted position, which is not possible with grooved heat pipes, a strong nucleate boiling limitation is observed for rather small heat fluxes. These observations shall be investigated more accurately to understand the physical mechanisms responsible for this behaviour.

Figure 1 :Figure 2 :

 12 Figure 1: Schematic of the screen mesh FPHP

Figure 3 :

 3 Figure 3: Schematic of the experimental bench

  presents the temperature profile along the heat pipe having only one screen mesh for 5 powers (Q = 7,3 W ; Q = 11,4 W ; Q = 15,9 W ; Q = 18,2 W ; Q = 19,4 W) in horizontal position. Locations of the heat sink and the heat source are

Figure 4 :

 4 Figure 4: Temperature profile along the heat pipe with one screen mesh layer in horizontal position

Figure 5b :

 5b Figure 5b: Zoom of figure 5a with linear fitted curves

Figure 7 :

 7 Figure 7: Influence of the heat sink nature on the characteristics of the heat pipe n°1 with two mesh screen layers (Q=15 W)

Figure 8 :Figure 9

 89 Figure 8: Maximal temperature difference vs. power; horizontal position (heat pipe n°1 with two mesh screen layers)

Figure 9 :

 9 Figure 9: Temperature field for different tilt angles (Q=15 W, heat pipe n°1 with two screen meshes)

Figure 10 :

 10 Figure 10: Temperature field along the heat pipe n°2 in horizontal position

Figure 11 presents

 11 Figure 11 presents temperature profiles obtained along the FPHP inclined by 15° from the horizontal position, the heat source being above the heat sink. The FPHP has been tested by increasing gradually the power from Q = 2.0 W to Q = 41.0 W. The thermal resistance decreases slowly from 0.2 K/W to 0.05 K/W until a threshold value of 40 W. Similarly to the horizontal position, beyond this power, a sudden dryout occurs on the whole capillary structure and the thermal resistance reaches a value of 0.24 K/W.

Figure 11 :

 11 Figure 11: Temperature profile along the heat pipe n°2 inclined by 15° from the horizontal


N Besic

G Vasile

J Chanussot

S Stankovic

J.-P Dedieu

G D'urso

D Boldo

J.-P Ovarlez

DRY SNOW BACKSCATTERING SENSITIVITY ON DENSITY CHANGE FOR SWE ESTIMATION

Keywords: SAR, backscattering, SWE, sensitivity, snow density

This paper provides comprehensive analysis of the dry snow pack backscattering coefficient dependence on the density change, for various SAR sensor parameters and chosen dry snow pack parameters, characteristic for the region of French Alps. As the result, qualitative conclusions, based on applying fundamental scattering theories (Rayleigh scattering model, Quasi Crystalline Approximation, Integral Equation Model) on the particular distributed target are presented. They represent the ground for semi-empirical models, which may provide a satisfactory link between backscattering coefficient and snow density (as one of the quantities defining SWE), as well as the guidelines for the further radar acquisitions over the Alpine region in France.

INTRODUCTION

Snow water equivalent (SWE) is defined as the depth of the layer of liquid water that would be produced if all the ice in the snow pack were melted [START_REF] Rees | Remote Sensing of Snow and Ice[END_REF]. It is function of two independent physical quantities, which characterise the snow pack: density (ρ s ) and depth(d):

SW E = 1 ρ w d 0 ρ s dz (1)
with ρ w as liquid water density. SWE estimation is important due to the wide usage of this kind of water resource in agriculture, power production, as the drinking water supply etc. Due to the numerous difficulties in performing "in situ" measurements (high altitudes, global spatial distribution), the estimation of this quantity turns out to be suitable for SAR remote sensing application [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part I: Inferring Snow Density and Subsurface Properties[END_REF][START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part II: Inferring Snow Depth and Particle Size[END_REF]. In order to be able to deduce SWE, as a physical quantity, from the SAR image, it is This work was supported by the French National R&DProgram TSEN-X PEPS UJF-CNRS 2011. necessary to relate both the snow density and the depth to the backscattering coefficient. This may represent a problem, due to the fact that backscattering is a function of many parameters, both sensor (frequency, polarization, angle) and target ones. This paper addresses one particular target parametersnow density.

More concretely, it deals dry snow density, where dry snow can be defined as snow consisted just of the ice crystals embedded in air, without any liquid water. Dry snow dielectric constant (eq.2) is a real number, which indicates the absence of absorption losses. It is a function of dry snow density (ρ ds ), which could be expressed through the ice volume fraction (f ice ) and the ice dielectric constant (ρ ice ). Due to the backscattering dependence on target dielectric properties through medium boundaries influence on electromagnetic waves propagation (Fresnel transmission coefficient, snow and underlying ground surface scattering), the dielectric constant appears to be the first link between the snow density and the backscattering coefficient.

ε ds = 1 + 1.9ρ ds = 1 + 1.9ρ ice f ice (2)
Aside from this, density also defines snow medium extinction properties (κ e ), introduced through radiative transfer equation:

dI( r, s) ds = -κeI( r, s) + 4π P ( r, s )I( r, s ) dΩ (3)
which models electromagnetic waves propagation through some particular medium. Change of EM wave intensity depends on the extinction, represented by the first term, and the amount of scattered radiation which is being re-scattered into the direction of interest, described by the second term using phase matrix P ( r, s ). Extinction losses, generally related to the absorption and the scattering losses, in the case of dry snow refer only to the losses due to the scattering. This can be justified by the lack of liquid water and the ice crystals dielectric properties (purely real dielectric constant). This paper threats two volume scattering types in parallel. First, single independent scattering assumption, characteristic for Rayleigh scattering model, which considers that the waves scattered of the particle do not affect other particles scattering. It can be considered as valid as far as the medium density is not significantly big, which makes it suitable for dry snow analysis. Second, multiple scattering assumption, modelled by Quasi Crystalline Approximation (QCA), which doesn't neglect the influence of the scattered waves on other particles scattering. Furthermore, it assumes waves coherence, and it stays valid even in the case of denser media [START_REF] Ao | Electromagnetic Wave Scattering by Discrete Random Media with Remote Sensing Applications[END_REF]. Two volume scattering types are characterized with two different functions of extinction coefficient against snow density. Therefore, the parallel study turns out to be quite significant for proper understanding of snow cover backscattering mechanism. The important remark would be that the study is based on the ice particles spherical shape assumption, which simplifies extinction derivation. The particles radius is taken as a function of snow sphericity (s) and dendricity (d) [START_REF] Longepe | Snowpack Characterization in Mountainous Regions Using C-Band SAR Data and a Meteorological Model[END_REF]:

r ice = d + (1 -d)(4 -s)[10 -4 m] (4)
The backscattering simulator, described in this paper, and used to draw qualitative conclusions concerning snow density influence on total backscattering in three microwave bands (L, C and X), is integrating two previously described links.

BACKSCATTERING MECHANISM

Total backscattering (σ 0 ) of the snow pack as a distributed target can be decomposed as the sum of the four components [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part II: Inferring Snow Depth and Particle Size[END_REF][START_REF] Fung | Microwave scattering and emission models for users[END_REF] (fig.

σ 0 = σ s + σ gr + σ v + σ gv (5)
For co-polarized channels (pp = hh ∨ vv) the backscattering components are given as [START_REF] Fung | Microwave scattering and emission models for users[END_REF]:

σs = σ(ε 0 , θ i , θ i , φs -φ, εs ε 0 , σ s RM S , l s c ) (6)
σgr = µ i µr T 2 pp (θr, θ i )e ( -2κed
µr ) σ(εs, θr, θr, φs -φ, εg εs , σ g RM S , l g c ) (7)

σv = a µ i 2 T 2 pp (θr, θ i )[1 -e ( -2κed
µr ) ]Ppp(µr, -µr, φs -φ) (8)

σ gv = µ i aRpp(θr, θ i , εg) κed µr e ( -2κe d µr )-4k 2 σ s RM S µ 2 r • T 2 pp (θr, θ i )Ppp(-µr, -µr, φs -φ) (9)
σ gv = µ i aRpp(θr, θ i , εg) κed µr e

( -2κe d µr )-4k 2 σ s RM S µ 2 r • T 2 pp (θr, θ i )Ppp(µr, µr, φs -φ) (10)
Snow pack surface backscattering coefficient (eq.6) is calculated using Integral Equation Model (σ) as a function of local incidence elevation angle (θ i ), azimuth angle (φ s ), snow dielectric constant, surface root mean square hight (σ s RM S ) and its correlation length (l s c ) [START_REF] Fung | Microwave scattering and emission models for users[END_REF]. The backscattering strongly depends on the incident waves wavelength, which makes it also a function of the incident media dielectric constant (ε 0 ).

For better comprehension of underlying ground backscattering component (eq.7), three different impacts on backscattering coefficient can be distinguished: -Air-snow interface direct impact, represented through the incident and refracted angle (θ r ), cosines ratio ( µi µr ) and squared Fresnel transmission coefficient (T 2 pp (θ r , θ i )), both affected by the density through the snow dielectric constant.

-Snow medium propagation impact , meaning the extinction (e ( -2κed µr ) ) given as a direct density function.

-Ground surface backscattering in the presence of snow, derived by applying the same model as in the case of snow surface. The presence of snow, through snow dielectric constant, defines the refracted angle (behaving as an incidence one at the ground surface), refracted wave wavelength and groundsnow dielectric contrast ( εg εs ). Volume backscattering component (eq.8) is also affected by air-snow boundary transmission, but importantly, it is dependent on snow density through extinction losses. It is function of normalized (relative to the scattering coefficient) Rayleigh phase matrix (P pp (µ r , -µ r , φ s -φ)), giving the amount of energy scattered in the backward direction.

Component named ground-volume interaction is related to the waves directed by the volume and then specularly reflected toward the antenna (eq.9) and the waves specularly reflected of the ground and then redirected toward the direction of interest by the volume (eq.9). Specular reflection is introduced through Fresnel reflection power coefficient R pp (θ r , θ i , ε g ) corrected with a factor 4k 2 σ s RM S µ 2 r which brings the terrain roughness into the account. Direction change caused by volume is modelled via normalized Rayleigh phase matrix.

BACKSCATTERING SIMULATOR

The built simulator is based on the previously described backscattering mechanism. Integral Equation Model (IEM) is Input data, chosen according to the available data, provided by EDF (Electricite de France) and according to the regional Meteo France forecasts are given in the table 1.

Surface RMS height represents an exception. Namely, 10 mm ground RMS height doesn't correspond precisely to the actual terrain roughness. The limits of IEM model and the necessity to use the same surface properties for each frequency band caused the choice of a limiting value for 10 GHz frequency.

2π λ σ RM S < 3 (11)

4. RESULTS

Fig. 2. σ gr share in total backscattering

In all three frequency bands, the absolutely most dominant component is the underlying ground one (fig. 2). This is particularly true for the L band, because both snow pack surface and volume component are increasing with the increase in frequency. The most important question is then how the snow density affects this component, which can be equalized with the whole backscattering coefficient, with the insignificant error.

L band

In the L band, backscattering (underlying ground backscattering) is rising with the snow density increase. This phenomenon was noticed first time by Shi and Dozier [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part I: Inferring Snow Density and Subsurface Properties[END_REF] and can be explained by the fact that density affects backscattering dominantly through the change of air-snow interface refraction angle and the change of the wavelength in the snow medium. Snow density increase causes increase of snow dielectric constant, which defines electromagnetic waves phase velocity. Taking the relation between frequency and wavelength, it can be seen that increased dielectric constant, through decrease of waves phase velocity, causes wavelength shortening. In backscattering theory, smaller wavelength implies bigger apparent roughness and therefore stronger backscattering. According to Snell-Descartes law waves incident and refracted angle relation at the boundary between two different medium is given as:

sin(θi) sin(θr) = εr εi ( 12
)
Snow cover is considered as refracted waves medium, implying that its dielectric constant increase leads to refracted angle decrease. Knowing that surface backscattering coefficient function against angle in L band has a negative slope, two previously described effects can justify the behaviour spotted in figure 3.

There is one more parameter potentially causing backscattering rise with density increase -extinction coefficient. By using two mentioned approaches in parallel, this possibility is declined. Namely, the backscattering curves for two models are approximately the same, which proves negligibility of the extinction and justifies figure.

Using this conclusion, increased sensitivity to the angle and wavelength change, Shi and Dozier created a model for deducing snow density from snow dielectric constant [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part I: Inferring Snow Density and Subsurface Properties[END_REF].

C band

In the C band, however, for the same assumed roughness parameters, the previously mentioned effect is not present any more. Now, density increase causes decrease of backscattering (fig. 3).

Comparison between independent and multiple scattering approaches is again pointing to the extinction negligibility, Fresnel transmission coefficient is independent of frequency, which leaves only ground surface backscattering in the presence of snow behaviour change as the cause of the sensitivity direction change.

Snow density change can affect ground surface backscattering in the presence of snow by: -changing ground incident waves wavelength and incident First effect, unlike it was in the case of L band, is not causing dramatic rise of backscattering. The explanation can be found in the fact that increase in frequency, supported by wavelength shortening leads to the surface backscattering angular distribution isotropy, which makes angle change to be almost insignificant for the backscattering. On the other side, ground-snow dielectric contrast decrease, which is the consequence of density increase, leads to the backscattering decrease (fig. 4).

X band

In X band underlying ground component dominance is still maintained and the sensitivity direction remains the same as in C band, but significantly increased (fig. 3).

The justification is derived from ground surface backscattering in the presence of snow. Sensitivity related to the change of the dielectric contrast is independent of frequency, so it keeps the same direction and value as the one presented for C-band. On the other side, ground incident waves wavelength and incident angle change is having contra effect from the one characteristic for L band. Snow density increase causes backscattering decrease, due to the change of surface backscattering against angle function which slope becomes positive with frequency increase (fig. 4).

CONCLUSION

The conclusion could be made that in C band, unlike the L [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part I: Inferring Snow Density and Subsurface Properties[END_REF], snow density dominantly affects total backscattering through the change of snow dielectric constant, which reflects to the change of ground-snow dielectric contrast. X band dry snow backscattering is characterized with the significant decrease of backscattering coefficient due to the density increase. Even the sensitivity is much bigger then the one found in L or C band, density impact is quite complex, because of approximately equal contribution of ground-snow dielectric contrast change and the change of ground incidence waves due to the presence of snow.

1 ): 1 .Fig. 1 .

 111 Fig. 1. Snow pack backscattering mechanism

  used for simulating surface backscattering, with the assumption of exponentially correlated surface. Rayleigh scattering model and Quasi Crystalline Approximation are modelling snow volume behaviour. The output result is the angular distribution of backscattering coefficient for different values of snow densitybackscattering sensitivity on the density change. Incidence angle values from 0 • up to 70 • are considered.

Fig. 3 .

 3 Fig. 3. Underlying ground backscattering component sensitivity on density change in L, C and X band, VV polarization

Fig. 4 .

 4 Fig. 4. σ gr in the presence of snow sensitivity on density change in C (left) and X (right) band, VV polarization

Table 1 .

 1 Simulation input parameters

	Input parameter	Value(s)
	Snow density	180,190,200,210,220 kg/m 3
	Snow depth	0.2 m
	Frequency	1.5 (L), 6 (C), 10 (X) GHz
	Particle sphericity	0.5
	Particle dendricity	0.5
	Ice dielectric constant	3.15
	Snow RMS height	10 mm
	Snow correlation length	50 mm
	Ground dielectric constant	6
	Ground RMS height	10 mm
	Ground correlation length	50 mm


N Besic

G Vasile

J Chanussot

S Stankovic

J.-P Ovarlez

G D'urso

D Boldo

J.-P Dedieu

STOCHASTICALLY BASED WET SNOW MAPPING WITH SAR DATA

Keywords: SAR, backscattering, wet snow, mapping, stochastical model

This paper proposes the new method for wet snow mapping using SAR data. It represents a modified version of the existing Nagler's mapping method, based on winter/summer image comparison, which is considered as the classic one. Instead of the existing unique threshold, a variable threshold matrix (function of the local incidence angle for each pixel) is proposed, based on dry and wet snow backscattering simulation results. The new membership decision method (with the respect to the dry/snow classes) is introduced. It considers the intensity ratio as a stochastical process: the probability that "the intensity ratio is smaller than the corresponding dry/wet snow determined threshold" is larger than the desired confidence level.

INTRODUCTION

Depending on liquid water content, snow can be considered as dry or wet. Former is defined as snow consisted just of the ice crystals embedded in air, without any liquid water, and its presence is characteristic for temperatures below 0 • C. The latter can be found during the melting season, when temperature exceeds 0 • C, and it contains certain amount of liquid water, introduced quantitatively through the percentage quantity called wetness (w).

Those two snow types, with respect to their dielectric properties, behave like two totally different materials. This is due to the fact that the wet snow contains liquid water with dielectric constant differing significantly from the one of the ice, causing the mixture to have different dielectric properties, also.

Dry snow cover can be characterized with dielectric constant, which is a function of dry snow density only [START_REF] Rees | Remote Sensing of Snow and Ice[END_REF] (ρ ds ):

ε ds = 1 + 1.9ρ ds = 1 + 1.9ρ ice f ice (1)
This work was supported by the French National R&DProgram TSEN-X PEPS UJF-CNRS 2011.

where ρ ds depends on ice volume fraction (f ice ), with ρ ice having a value 917kg/m 3 . Dielectric constant is purely real, indicating the absence of medium dielectric losses.

On the other side, wet snow dielectric constant is a complex quantity, function of ice volume fraction (f ice ), wetness (w) and frequency (f ) :

ε ws = ε ws + jε ws (2)
For the frequency range of 3GHz -15GHz it is [START_REF] Rees | Remote Sensing of Snow and Ice[END_REF]:

ε ws = 1 + 1.83ρ ds + 0.02w 1.105 + 0.073w 1.31 1 + ( f 9.07 ) 2 (3)
ε ws = 0.073 f 9.07 w 1.31 1 + ( f 9.07 ) 2 (4)
Unlike the dry snow one, wet snow dielectric constant, being a complex quantity, it has its imaginary part, indicating the presence of the medium absorption losses.

This difference is pointing out to the difference in backscattering mechanisms of those two snow cover types. When estimating snow pack parameters by SAR remote sensing the proper identification of the backscattering mechanism is required. In the first processing step, it is necessary to be able to distinguish between the wet and the dry snow cover [START_REF] Longepe | Snowpack Characterization in Mountainous Regions Using C-Band SAR Data and a Meteorological Model[END_REF].

Nagler and Rott [START_REF] Nagler | Retrieval of wet snow by means of multitemporal SAR data[END_REF] proposed a dry/wet snow mapping method, using C band SAR data, founded on the fact that the backscattering coefficient should be smaller in case of a wet snow, due to the presence of the medium absorption. They introduced a single backscattering difference threshold, which allows forming the binary classification map. The latter is obtained in each pixel whenever the difference between a melting season SAR image (I 1 ) and a corresponding SAR summer image (I 2 ) is lower than -3 dB:

I 1 (i, j) I 2 (i, j) < 1 2 (5)
This paper proposes novel method, which introduces a variable threshold value (function of the local incidence angle (α) for every pixel). In our approach, the membership decision of a pixel (i, j), with respect to the dry/wet snow classes, is made by considering the intensity ratio as a stochastical process: the probability that the intensity ratio is smaller than the corresponding dry/wet snow determined threshold P ( I1(i,j) I2(i,j) < T (α(i, j))) is larger than the desired confidence level C.

Although the method verification was performed using X band data, there is an open assumption of its applicability in the C band.

METHODOLOGY

In our approach, the variable threshold is derived using the snow pack backscattering simulator based on fundamental scattering theories. Integral Equation Model [START_REF] Fung | Microwave scattering and emission models for users[END_REF] is used for the modelling of both snow surface backscattering and underlying ground backscattering. The Quasi Crystalline Approximation [START_REF] Ao | Electromagnetic Wave Scattering by Discrete Random Media with Remote Sensing Applications[END_REF] is used for snow volume behaviour modelling through the Radiative Transfer Theory [START_REF] Longepe | Snowpack Characterization in Mountainous Regions Using C-Band SAR Data and a Meteorological Model[END_REF]. In case of dry snow the approximation is applied in its basic form, while the wet snow simulator, due to the increase in dielectric contrast between the particles and the host medium, requires application of Quasi Crystalline Approximation with Coherent Potentials [START_REF] Ao | Electromagnetic Wave Scattering by Discrete Random Media with Remote Sensing Applications[END_REF]. Our simulator gives the total backscattering as the sum of particular backscattering components: snow pack surface component, underlying ground component, volume component and ground volume interaction component [START_REF] Shi | Estimation of Snow Water Equivalence Using SIR-C/X-SAR, Part II: Inferring Snow Depth and Particle Size[END_REF]. The final threshold value (T (α)) given in fig. 1

( nX mp ) n-1 (1 + nX mp ) n+p (6)
The underlying assumptions are two:

1) gaussianity of SAR clutter, 2) negligible interferometric coherence.

The algorithm uses the boxcar neighborhood coupled with approximate maximum likelihood estimators, in order to obtain local statistics for each of the areas in the image. The result of this operation are estimated parameters m, n and p (eq. 6) for each square neighbourhood in the image, and the mean average value of concerned pixels. This allows defining the corresponding cumulative distribution function (CDF) of the intensity ratio random variable. After having the CDF, it is possible to derive the probability that the ratio between wet snow and dry snow image is smaller then the threshold.

i out (i, j) = 1 µ T (i,j)µ -∞ p (i,j) (X)dX (7)
The resulting value is considered as wet snow probability. The presented probability map can be transformed into the wet snow binary map by defining the appropriate confidence level C (for example 0.95) (eq. 8).

I out (i, j) = 1 if i out (i, j) ≥ C 0 if i out (i, j) < C (8)

RESULTS

We illustrate the results obtained with the proposed dry/wet snow-mapping algorithm with 2 TerraSAR-X X-band images acquired in the winter of 2009 over the Grand Rousse massif near Grenoble, France. Fig. 2 illustrates the maps computed with TerraSAR-X, between February (08/02/2009) for dry snow and March (02/03/2009) for wet snow. For the purpose of comparison, it also provides corresponding binary maps, based on both single threshold and variable thresholds. The necessary remarque would be that the former binary maps can not be exactly classified as the most advanced previously known ones, given that the nonlinear activation function introduced in [START_REF] Longepe | Snowpack Characterization in Mountainous Regions Using C-Band SAR Data and a Meteorological Model[END_REF] to account for the influence of underlying media and pixel heterogeneity, was not applied.

METHOD VALIDATION ON REAL DATA

The verification of the proposed method validity is conducted using the local temperature measurements at the ground level. The measurements data, provided by EDF ( Électricité The procedure is based on the stated fact that wet snow presence is characteristic for the local temperature above 0 • C, while dry snow can be found below 0 • C. Using local incidence angle data the temperature measurements are projected into the slant range and then compared to the result of method application on corresponding winter and melting season -wet snow probability map (fig. 3). The approximate matching between the high temperature regions and the high probability regions, two information sources which could be considered as independent, is pointing to the validity of the proposed method.

CONCLUSIONS

This approach is based on the multitemporal data comparison, just like the classical one proposed in [START_REF] Nagler | Retrieval of wet snow by means of multitemporal SAR data[END_REF]. One improvement consists in the choice of the reference image. Instead of using the bare ground (summer season) image as reference, dry snow image is taken (winter season). According to our backscattering simulator results, the assumption that bare ground and dry snow backscattering difference is always smaller than -3 dB is not valid for the X band (fig. 4). That implies that bare ground and melting season image backscattering coefficient difference bigger than 3 dB is not unambiguously pointing to the wet snow. Therefore, the comparison is made directly between the assumed pure dry snow cover image and the mixed snow cover one. Variable threshold, introducing important local incidence angle influence reinforces the decision validity, while the stochastically based decision method enhances discrimination accuracy, additionally.

  is obtained by averaging backscattering coefficient over different ground dielectric constant and wetness values, characterizing the French Alps.

Fig. 1 .

 1 Fig. 1. Threshold angular distribution for the HH and the VV co-polarizations

Fig. 2 .

 2 Fig. 2. Wet snow mapping

Fig. 3 .

 3 Fig. 3. Method validation: Wet snow probability map (HH and VV) and temperature map

Fig. 4 .

 4 Fig. 4. Bare ground (red) backscattering and dry snow backscattering for different densities (green)