H Ayed

A Mifdaoui

C Fraboul

Hierarchical Traffic Shaping and Frame Packing to Reduce Bandwidth Utilization in the AFDX

Keywords: CAN, AFDX, RDC, Hierarchical Traffic Shaping, Frame Packing, Schedulability analysis, Optimization process

The increasing complexity and heterogeneity of avionic networks make resource savings a challenging task to guarantee easy incremental design during the long lifetime of an aircraft. In this paper, we focus on the optimization of interconnection devices for multi-cluster avionic networks, called Remote Data Concentrators (RDC), and especially for the CAN-AFDX network. The design of this optimized RDC device consists in implementing frame packing strategies to manage upstream (sensors) flows to improve bandwidth utilization in the AFDX; and Hierarchical Traffic Shaping (HTS) algorithm to control downstream (actuators) flows to guarantee bandwidth isolation on CAN. Schedulability analysis integrating the effects of these new mechanisms is detailed and validated. Furthermore, a heuristic approach to tune the Hierarchical Traffic Shaping parameters within the RDC device is proposed to reduce as much as possible bandwidth utilization in the AFDX, while ensuring flows schedulability. The performance analysis conducted on a realistic avionic case study proves the efficiency of the optimized RDC device to reduce bandwidth utilization in the AFDX, compared to the basic device currently implemented in avionics.

I. INTRODUCTION

A. Context & Motivations

The complexity of avionic communication architecture is increasing inherently due to the growing number of interconnected end-systems and the expansion of exchanged data. To be effective in meeting the emerging requirements in terms of bandwidth, latency and modularity, the current avionic communication architecture, shown in Figure 1, consists of an AFDX backbone network to interconnect the critical avionic end-systems and some Input/ Output (I/O) data buses. Clusters are then interconnected via specific devices, called Remote Data Concentrators (RDCs), standardized as ARINC655 [START_REF] Committee | Remote Data Concentrator (RDC) Generic Description[END_REF]. RDC devices are modular gateways distributed throughout the aircraft to handle heterogeneity between the AFDX backbone and I/O data buses.

Although RDC devices enhance avionics modularity and reduce maintenance efforts, they become in the same time a major challenge in the design process of such multi-cluster avionic architectures. Implemented RDC in new generation aircraft, such as the A400M or A350 is based on a naive frameconversion strategy, called (1:1) strategy, where each non-AFDX frame is converted to an AFDX frame and vice-versa. This strategy is simple to implement, however it implies high network-resource use, and especially significant bandwidth utilization in the AFDX. This feature is important for avionic applications to guarantee easy incremental design and enhance margins for future avionic functions additions. Therefore, the design of an optimized RDC device integrating resource saving mechanisms becomes a necessity to enhance the scalability and performances of avionic applications.

In [START_REF] Ayed | Frame Packing Strategy within Gateways for Multi-cluster Avionics Embedded Networks[END_REF], as a first step the authors introduced an optimized RDC device implementing a novel dynamic frame packing strategy based on a waiting timer, called Fixed Waiting Time (FWT) strategy. Results for a representative avionic case study showed a noticeable improvement of system performance, compared to classic RDC device with a simple (1:1) strategy. Then, to obtain further enhancements in terms of bandwidth utilization in the AFDX, an accurate static frame packing strategy, called Messages-Set Partitioning (MSP) strategy, was integrated [START_REF]Interconnection optimization for multi-cluster avionics networks[END_REF]. The optimized RDC device implementing the MSP strategy induces significant bandwidth utilization reduction, compared to the one implementing the FWT strategy. In this previous work, two main assumptions were considered: (i) ignoring the contentions on I/O data buses between upstream and downstream flows, i.e., incoming (and outgoing) flows to (and from) AFDX calculators from sensors (to actuators, respectively), by considering specific data buses either for sensors or actuators; (ii) RDC device can interconnect only one I/O data bus to the AFDX.

In this paper, the design of such an optimized RDC device is extended to cover the general case where: (i) I/O data buses are shared between sensors and actuators; (ii) an RDC Under these new assumptions, First results for a CAN-AFDX case study concerning bandwidth utilization in the AFDX are illustrated in Figure 2. These results are obtained when varying the CAN load and using MSP strategy to pack upstream frames within RDC device, with reference to (1:1) strategy. Scenarios 1 and 2 represent two configurations of priority assignment of upstream and downstream flows on CAN. The former is when upstream flows have higher priority than downstream flows, where the latter represents the inverse.

Under scenario 1, we still observe a significant reduction of bandwidth utilization in the AFDX when using the optimized RDC device implementing MSP strategy, compared to the basic one with (1:1) strategy. Hence, under this priority assignment configuration, our proposal in [START_REF]Interconnection optimization for multi-cluster avionics networks[END_REF] is still efficient. However, with scenario 2, the performance of the optimized RDC device is degraded and becomes equivalent to the basic RDC device performance under high CAN load (from 36 %). To understand the reasons of this degradation, let's take a look on the Worst-Case Response Times (WCRT) on CAN of upstream flows, shown in Figure 3. As can be noticed, WCRTs increase significantly under scenario 2 because of contentions with higher priority downstream flows. However, increasing upstream flows delays on CAN is not in favor of performing frame packing within RDC device, and consequently of reducing bandwidth utilization in the AFDX.

In avionics context, the modification of application specifications can ramify maintenance efforts and incremental design process. Therefore, revising priority assignment of different flows to improve system performances can be a complicated task for designers. Our aim consists in reducing as much as possible bandwidth utilization in the AFDX induced by the RDC device, even in the worst-case scenario of priority assignment for upstream flows, i.e., upstream flows have lower priority than downstream flows. Therefore, to overcome the limitations highlighted with these first results, the key idea is favoring frame packing mechanism for upstream frames within RDC device to reduce bandwidth utilization in the AFDX. This fact consists in minimizing as much as possible WCRTs on CAN of upstream flows when having the low priority, and ensuring at the same time the temporal constraints of downstream flows.

To minimize the interference from downstream flows on the transmission of upstream flows on CAN, and consequently the WCRTs on CAN of upstream flows, we propose the usage of Hierarchical Traffic Shaping (HTS) algorithm [START_REF] Zeng | A hierarchical traffic shaper for packet switches[END_REF] within RDC device. This algorithm will control downstream flows transmission on CAN, and consequently guarantee bandwidth isolation between upstream and downstream flows. HTS algorithm consists of a set of traffic shapers, based on the leaky bucket method [START_REF] Turner | New Directions in Communications (or Which Way to the Information Age?)[END_REF], and connected in a hierarchical way according to a tree structure. HTS algorithm is a special case of hierarchical server-based scheduling which has been successfully implemented in various network applications [START_REF] Zeng | A hierarchical traffic shaper for packet switches[END_REF] [6] [7]. This paper extends the use of this algorithm within avionic RDC devices to control downstream flows and consequently to reduce bandwidth utilization in the AFDX, induced by upstream flows. This HTS algorithm implements two levels of traffic shaping. The first level is based on greedy method [START_REF] Wandeler | On the Use of Greedy Shapers in Real-Time Embedded Systems[END_REF] which comes for free, to control individual downstream flows, and consequently to reduce the jitter due to the AFDX network [START_REF] Davis | Traffic Shaping to Reduce Jitter in Controller Area Network (CAN)[END_REF]; where the second level is used to shape aggregate downstream flows, scheduled according to fixed priority nonpreemptive policy, to substantially reduce the number of flows introducing interference on upstream flows on CAN.

B. Original Contributions

The contribution of this work are:

• The design of an optimized RDC device implementing:

(i) frame packing strategies to manage upstream flows to reduce bandwidth utilization in the AFDX; (ii) Hierarchical Traffic Shaping (HTS) algorithm to control downstream flows for minimizing interferences and ensuring bandwidth isolation on CAN;

• The schedulability analysis for upstream and downstream flows integrating the effects of frame packing and HTS algorithm within the RDC device;

• A heuristic approach to tune the HTS parameters to minimize as much as possible bandwidth utilization in the AFDX while ensuring flows schedulability;

• The validation of the optimized RDC device performances through a realistic avionic case study.

C. Paper Organization

In the next section, we give an overview of AFDX and CAN technologies and review the most relevant work in the domain of Hierarchical Traffic Shaping in networks. Afterwards, in Section III, we explain the main concepts of Hierarchical Traffic Shaping algorithm and its integration in the RDC device. In Section IV, we present the schedulability analysis of upstream and downstream flows in this case. Section V describes the tuning process of Hierarchical Traffic Shaping parameters. Finally, in section VI, we conduct performance analyses to evaluate the efficiency of our proposal to improve resource savings in the AFDX for a realistic avionic case study.

II. BACKGROUND AND RELATED WORK

In this section, we give an overview of AFDX and CAN technologies and review the most relevant work in the domain of Hierarchical Traffic Shaping in networks.

A. Network Technologies

The AFDX [START_REF] Committee | Aircraft Data Network Part 7, AFDX NETWORK, ARINC Specification[END_REF] network is based on the Full Duplex Switched Ethernet protocol at 100Mbps. This technology manages the large amount of exchanged data through policing mechanisms added in switches and the Virtual Link (VL) concept. This concept provides a way to reserve a guaranteed bandwidth for each traffic flow. The VL represents a multicast communication which originates at a single end-system and delivers packets to a fixed set of end-systems. Each VL is characterized by: (i) BAG (Bandwidth Allocation Gap), ranging in powers of 2 from 1 to 128 milliseconds, which represents the minimum inter-arrival time between two consecutive frames; (ii) MFS (Maximal Frame Size), ranging from 64 to 1518 bytes, which represents the size of the largest frame that can be sent during each BAG.

CAN native protocol [START_REF] Gmbh | CAN specification Version[END_REF] is a 1 Mbps data bus that operates according to an event-triggered paradigm where messages are transmitted using a priority-based access mechanism. Collisions on the bus are resolved following a CSMA/CR protocol (Carrier Sense Multiple Access/Collision Resolution) thanks to the bit arbitration method. CAN frame includes a payload up to 8 bytes and an overhead of 6 bytes due to the different headers and bit stuffing mechanism.

B. Hierarchical Traffic Shaping in Networks

The Hierarchical Traffic Shaping (HTS) is a part of general Hierarchical Server-Based (HSB) Scheduling: each traffic shaper in the hierarchy structure is considered as a server which will bound the traffic burstiness sent within a limited time window. HSB scheduling is a common approach that has been used in many network applications to control interference between various traffic classes with different real-time requirements, i.e., Soft Real-Time (SRT) and Hard Real-Time (HRT) traffic.

Concerning industrial application and especially Real-Time Ethernet, one of the most relevant approaches based on HSB framework to guarantee a dynamic adaptation of servers was proposed in [START_REF] Iqbal | Implementing hierarchical scheduling on cots ethernet switches using a master/slave approach[END_REF]. The authors presented a multi-level HSB architecture for Ethernet, implemented on commercial switches and based on FTT-SE (Flexible Time Triggered Switched Ethernet) paradigm [START_REF] Marau | Enhancing Real-time communication over COTS Ethernet switches[END_REF]. Schedulability analysis was detailed and validated using experimentation. This approach is efficient in dynamic environment, and typically open networks. The servers parameters are assumed to verify a priori traffic temporal constraints.

In automotive applications, various approaches based on traffic shaping and HSB scheduling were proposed to improve CAN bus performances. In [START_REF] Davis | Traffic Shaping to Reduce Jitter in Controller Area Network (CAN)[END_REF], traffic shaping algorithm based on leaky bucket method, and particularly greedy method [START_REF] Wandeler | On the Use of Greedy Shapers in Real-Time Embedded Systems[END_REF], was integrated within gateways to reduce the jitter on the destination network and improve the schedulability of lower priority messages. However, this approach is considered as a limited form of HTS approach implementing only one level of traffic shapers to control individual input messages. In [START_REF] Nolte | Server-based scheduling of the CAN bus[END_REF], HSB scheduler, based on earliest deadline first algorithm, was detailed to use CAN in a more flexible way compared to the native CAN. This approach improved bandwidth isolation among aperiodic traffic and was validated using simulation. Analytical approach to provide worst-case response times of messages and to guarantee messages schedulability was lacking.

In avionics application, traffic shaping is integrated in AFDX end-systems to guarantee a reserved bandwidth for each application and is standardized as Virtual Link concept. This approach guarantees bandwidth isolation between traffic flows and improve the predictability of the AFDX network. In this paper, we extend this approach by implementing HTS scheduling within RDC devices to interconnect AFDX backbone with I/O CAN buses. The main idea is to minimize the interference from downstream flows on the transmission of upstream flows on CAN, and consequently the WCRTs on CAN of upstream flows. This will favor frame packing mechanism for upstream frames within RDC device and consequently will reduce bandwidth utilization in the AFDX. Our proposal consists of two traffic shaping levels and a root server to implement native CAN scheduler. The idea of the first level of traffic shapers is similar to the one detailed in [START_REF] Davis | Traffic Shaping to Reduce Jitter in Controller Area Network (CAN)[END_REF] where we consider greedy method, which does not increase maximum end-to-end delays as proved in [START_REF] Wandeler | On the Use of Greedy Shapers in Real-Time Embedded Systems[END_REF], and reduce the jitter induced by the AFDX network. However, we extend this implementation by adding a second level of traffic shapers to substantially reduce the number of flows introducing interference on upstream flows on CAN. The schedulability analysis of upstream and downstream flows is proved and validated through a realistic avionic case study. Furthermore, unlike [START_REF] Iqbal | Implementing hierarchical scheduling on cots ethernet switches using a master/slave approach[END_REF], a tuning process of the HTS parameters is proposed to minimize as much as possible bandwidth utilization in the AFDX while ensuring flows requirements.

III. HIERARCHICAL TRAFFIC SHAPING WITHIN RDC

DEVICES

In this section, we first give an overview of the RDC architecture with the different implemented mechanisms. Then, the integration of Hierarchical Traffic Shaping (HTS) algorithm within the RDC device is detailed. Finally, the HTS modeling is described.

A. RDC Architectural overview

The proposed RDC device implements:

• frame packing strategies to manage upstream flows to reduce bandwidth utilization in the AFDX;

• Hierarchical Traffic Shaping (HTS) algorithm to control downstream flows for minimizing interferences and ensuring bandwidth isolation on CAN;

• support of multiple I/O networks using partitioning to provide the required safety level by ensuring that an errant I/O network running in one partition will not affect the others. As shown in Figure 4, for each I/O network, upstream flows are first processed by the Frame Packing unit, implementing MSP strategy [START_REF]Interconnection optimization for multi-cluster avionics networks[END_REF]. This latter is illustrated in Figure 5 and consists in defining off-line input frame partitioning where each sub-partition represents the associated subset of an output frame. Then, based on a static mapping table, one Virtual Link is associated to multiple CAN messages. The frame packing is synchronized with the reception of the most urgent input frame among each defined sub-partition. A timeout is implemented to avoid losing all the accumulated messages in case of nonreception of the most urgent one. This strategy will reduce the induced overhead in the AFDX, and consequently bandwidth consumption. Afterwards, the Rx Buffer of the associated partition stores the incoming frames in FIFO (First In First Out) order. The role of the I/O Central Processing Unit (CPU) is to move packets for the incoming Rx buffers to the outgoing Tx buffer of the AFDX interface. For downstream flows, the I/O CPU move packets from the incoming AFDX Rx buffer to the corresponding partition Tx Buffer, based on the forwarding table. Then, these received packets are processed within Unpacking Frame unit, detailled in Figure 6. This latter extracts one or many elementary data from the same AFDX frame depending on the data packing performed within the initial AFDX source [START_REF] Sheikh | Optimal Design of Virtual Links in AFDX Networks[END_REF], i.e., generated data from different AFDX applications hosted by the same end-system can be grouped within the same AFDX frame to minimize communication delay and bandwidth utilization in the AFDX. Afterwards, based on static mapping table, CAN identifiers are defined. Hierarchical Traffic Shaping unit is performed to eliminate the jitter due to the AFDX network and to minimize interference on CAN. This unit is detailed in the next section.

B. Hierarchical Traffic Shaping Structure

The HTS structure is based on a set of traffic shapers and servers connected in a tree structure and defined in a static manner a priori, as shown in Figure 7. This latter is organized into three levels: leaf, inner and root.

• Leaf traffic shapers are implemented to control incoming packets from the AFDX interface of the RDC device. They are based on greedy method [START_REF] Wandeler | On the Use of Greedy Shapers in Real-Time Embedded Systems[END_REF] which comes for free, i.e., does not increase maximum end-to-end delays. However, they reduce efficiently the observed jitter up their reception at the RDC device [START_REF] Davis | Traffic Shaping to Reduce Jitter in Controller Area Network (CAN)[END_REF]. This fact enhances lower priority messages schedulability on CAN. These shapers are based on leaky bucket method and offer to incoming packets the same guarantees than the associated AFDX Virtual Link. Hence, at the output of these traffic shapers, the minimum inter-arrival time between packets is equal to the corresponding BAG and the maximum frame size is bounded.

• Each inner traffic shaper is based on leaky bucket method to shape aggregate downstream flows of outgoing packets from leaf shapers after being classified and scheduled according to fixed priority non-preemptive policy. The aim of these shapers is to substantially reduce the number of flows introducing interference on upstream flows and to guarantee bandwidth isolation on CAN. One or many inner traffic shapers can be implemented depending on the incoming traffic rate. Indeed, shaping all the incoming flows using the same inner traffic shaper will induce small inter-arrival time between packets at the output, and consequently important interference with upstream flows. The tuning process of these inner shapers will be detailed in Section V.

• The root server implements simply fixed priority nonpreemptive scheduling which represents the CAN native behavior. All the packets will be multiplexed at the root server according to their corresponding priorities.

C. Hierarchical Traffic Shaping Modeling

Consider S up and S down for upstream and downstream flow sets, respectively. For any stream flow m ∈ S up ∪ S down , we associate four characteristics {T m , L m , Dl m , P m } which represent period, maximum payload, deadline and priority used to access to the CAN bus, respectively. We consider a strict order of CAN priorities, i.e., for any two messages m k and m j , P m k < P mj means that message m k has higher priority than m j .

The HTS is used to manage only downstream flows to minimize interference with upstream flows on CAN. Each leaf traffic shaper is applied for only one type of downstream flow and consequently admits the same period and authorized maximum payload than its associated flow. However, an inner traffic shaper is applied to a group of outgoing flows from leaf shapers. Then, each inner shaper sh in the set of inner shapers Sh inner is characterized by {T sh , L sh , Dl sh , P sh }, where:

• T sh is the period. This value is comprised between T min sh and T max sh depending on the characteristics of its input downstream flows set S sh . To support the aggregate flow rate, T max sh is at most equal to

1 i∈S sh 1 T i
. Furthermore, to avoid overflowing the CAN bus, we consider that T min sh is at least equal to 1ms, which is an arbitrary choice that integrates CAN transmission capacity and typical production periods of CAN sources. If

1 i∈S sh 1 T i
> 1ms, than this configuration is possible; else we need to investigate other HTS configurations;

• L sh is the maximum payload size where L sh = max i∈S sh L i ;

• Dl sh is the deadline and is equal to the period T sh ; • P sh is the associated priority to the inner shaper. This value depends on the considered communication way and is equal to P min sh or P max sh . To cover the worst-case from the downstream flows point of view, this priority is considered as the lower priority among all its input downstream flows set, P sh = P max sh = max

i∈S sh P i .
However, the worst-case from the upstream point of view corresponds to considering the higher priority among all its input downstream flows set, P sh = P min sh = min i∈S sh P i .

IV. SCHEDULABILITY ANALYSIS

In this section, we present the sufficient schedulability test to perform schedulability analysis of upstream and downstream flows. Then, we detail the timing analysis of upstream and downstream flows integrating frame packing and HTS algorithm effects. Finally, we give some numerical results and first conclusions on the optimized RDC performances.

A. Sufficient Schedulability Test

For avionic embedded applications, it is essential that the communication network fulfills certification requirements, e.g., predictable behavior under hard real-time constraints and temporal deadline guarantees. The use of a frame packing process and Hierarchical Traffic Shaping within the RDC will increase communication latencies and real-time constraints have to be checked. In order to deal with the worst-case performance analysis of such networks, we consider as metric the worstcase end-to-end delay that will be compared to the temporal deadline for each frame.

The end-to-end delay of each upstream and downstream flows consists of three parts, as shown in Figure 8: • d CAN : the Worst Case Response Time (WCRT) on CAN.

The classic schedulability analysis for a native CAN bus Fig. 8. end-to-end delay for upstream and downstream flows [START_REF] Davis | CAN schedulability analysis: Refuted, revisited and revised[END_REF] based on a Fixed Priority non-preemptive scheduler is considered in this paper;

• d RDC : the maximal duration the message might be delayed in the RDC. This delay depends on the communication way and the crossed RDC functions;

• d AF DX : the upper bound on the AFDX delay. A maximum bound on AFDX delay will be considered herein to simplify the schedulability analysis, using results in [START_REF] Grieu | Analyse et valuation de techniques de commutation ethernet pour l'interconnexion de systemes avioniques[END_REF]. The schedulability test is as follows:

∀m ∈ S up ∪ S down : d CAN (m) + d RDC (m) + max m (d AF DX (m)) ≤ Dl m (1)
where S up and S down are upstream and downstream flow sets, respectively.

Hence, the schedulability test becomes:

∀m ∈ S up ∪ S down , d CAN (m) + d RDC (m) ≤ Dl m -max m (d AF DX (m))(2)
For any message m, Dl m and max m (d AF DX (m)) are known. Therefore, in the next sections, we will focus on the upper bounds for d RDC (m) and d CAN (m), distinguishing upstream and downstream cases to verify the schedulability test 2.

B. Timing Analysis for Upstream Flows

First, the RDC device delay imposed to upstream flows is due to frame packing unit. The upper bound of this delay was detailed in [START_REF]Interconnection optimization for multi-cluster avionics networks[END_REF]. We proved that the worst-case waiting time for a CAN message m j in the RDC device occurs when it arrives immediately after the end of reception of the most urgent message m u in the RDC, i.e., m u is the message with the smallest period among the subset messages packed with m j in the same AFDX frame.

An upper bound of the waiting time in the RDC for CANmessage m j is:

W T (m j ) = 0 if j = u T u + d CAN (m u ) otherwise (3)
Therefore, the upper bound of RDC delay d RDC (m j ) is the sum of: (i) a technological latency due to payload extraction and relaying process, called ǫ; (ii) waiting time in the RDC between the reception instant of the CAN message and the transmission instant of its associated AFDX frame W T (m j ).

d RDC (m j ) = ǫ + W T (m j ) (4)
Then, the upper bound on WCRT on CAN of an upstream flow is computed using classic results for Fixed Priority nonpreemptive scheduler [START_REF] Davis | CAN schedulability analysis: Refuted, revisited and revised[END_REF]. However, we consider null jitter due to leaf shapers, based on greedy method and implemented in HTS structure.

For a message m ∈ S up ,

d CAN (m) = w(m) + C m ( 5
)
where C m is the maximum transmission time on CAN integrating the maximum payload size L m and the transmission capacity of CAN bus, and w(m) is the maximum queuing delay computed using the following expression:

w n+1 (m) = max k∈lep(m) C k + k∈hp(m) W n (m) T k * C k (6)
where lep(m) and hp(m) are the sets of messages with priorities lower or equal to m and with priorities higher than m, respectively.

We start with an initial value equal to w 0 (m) = C m and continue until obtaining one of these two situations: (i) if w n+1 (m) + C m > Dl m , then stop and conclude that m is not schedulable; (ii) if w n+1 (m) = w n (m), then stop and conclude that m is schedulable.

In our case, we have to identify clearly lep(m) and hp(m) for each message m ∈ S up to integrate the impact of output flows of each inner shaper in the HTS structure on its worstcase response time. For each message m ∈ S up ,

• hp(m) = {k ∈ S up ∪ Sh inner / P k < P m }: set of messages with priorities higher than m among upstream flows and inner shapers by considering P min sh for each inner shaper sh ∈ Sh inner ;

• lep(m) = {j ∈ S up ∪ Sh inner / P j ≥ P m }: set of messages with priorities lower or equal than m among upstream flows and inner shapers by considering P min sh for each inner shaper sh ∈ Sh inner . The schedulability test in 2 can be easily verified using Eq. 4 and 6.

C. Timing Analysis for Downstream Flows

The RDC device delay imposed to downstream flows is mainly due to the blocking time of the HTS algorithm. For each message m, first the leaf shaper, based on greedy method, comes for free and does not increase the end-to-end delay. Then, at the inner shaper sh, the worst-case blocking time is computed using the following iterative expression until convergence:

   B 0 shaper (m) = X m * T sh B n+1 shaper (m) = X m * T sh + k∈hpinner(m) B n shaper (m) T k * T sh
where,

X m = 0 if lp inner (m) = ∅ 1 otherwise
and,

• hp inner (m) = {k ∈ S sh / P k < P m }: set of messages shaped with the same inner shaper sh, with priorities higher than m;

• lp inner (m) = {j ∈ S sh / P j ≥ P m }: set of messages shaped with the same inner shaper sh, with priorities lower than m. The stop condition is B n+1 shaper (m) = B n shaper (m). This worst-case blocking delay is computed based on the classic model for Fixed Priority non-preemptive scheduler in [START_REF] Tindell | Calculating Controller Area Network (CAN) message response times[END_REF]. We consider in our case that any message m ∈ S sh will occupy the shaper during T sh because the shaper does not send more than one packet per T sh .

Therefore, the upper bound of RDC delay d RDC (m) is the sum of: (i) the technological latency due to payload extraction and relaying process, ǫ; (ii) the maximum blocking time of inner shape in the HTS structure, B shaper (m).

d RDC (m) = ǫ + B shaper (m) (7)
In the other hand, the upper bound on worst-case response time on CAN for a downstream flow still is computed using Eq. 5. However, the lep(m) and hp(m) for each message m ∈ S down to integrate the impact of upstream flows are as follows:

• hp(m) = {k ∈ S up ∪ Sh inner / P k < P m }: set of messages with priorities higher than m among upstream flows and inner shapers by considering P max sh for each inner shaper sh ∈ Sh inner ;

• lep(m) = {j ∈ S up ∪ Sh inner / P j ≥ P m }: set of messages with priorities lower or equal than m among upstream flows and inner shapers by considering P max sh for each inner shaper sh ∈ Sh inner . The schedulability test in 2 can be verified using Eq. 6 and 7.

D. Numerical Results

We consider an example of I/O CAN bus with downstream and upstream flows described in Tables I and II, respectively. This set of flows consists of 48 messages with payload equal to 8 Bytes and periods between 8 and 32 ms. We assume the worst-case priority assignment configuration for upstream flows, i.e., all downstream flows have higher priority than upstream flows.

!" !$ !%" !%$ !&" !&$ !*" &$ &' &N &( &O *" *% *& ** *) *$ *' *N *( *O )" )% )& )* )) )$ )' )N )( 0AM>D64F ;I44?JI!P- -I?C@93ID64F B2!Q>L 098R!Q>L
!" !$ !%" !%$ !&" !&$ !*" % & * ) $ ' N ( O %" %% %& %* %) %$ %' %N %( %O &" &% && &* &)

0AM>S-HC1!D64F

;I44?JI!P--I?C@93ID64F B2!Q>L 098R!Q>L Fig. 10. WCRTs of downstream flows on CAN

As illustrated in Figure 9, the WCRTs of upstream flows on CAN decrease when HTS algorithm is implemented within the RDC device, compared to the basic RDC device. This reduction is in favor of performing MSP strategy within RDC device, and consequently reducing bandwidth utilization in the AFDX as described in Table III. Indeed, using HTS algorithm and MSP strategy within the optimized RDC device offers a noticeable improvement on the induced bandwidth in the AFDX, where reductions of 40% and 30% are obtained compared to the basic RDC device, i.e., implementing (1:1) strategy, and the optimized RDC device implementing only MSP strategy, respectively.

However, this improvement on WCRTs of upstream flows on CAN, and consequently bandwidth utilization in the AFDX, induces a degradation of WCRTs of downstream flows as shown in Figure 10. The blocking time due to inner shapers does not respect the timing requirements of downstream messages with identifiers 7 and 8. Therefore, we need a tuning process of HTS parameters to minimize as much as possible bandwidth utilization in the AFDX while ensuring downstream flows schedulability.

V. HIERARCHICAL TRAFFIC SHAPING TUNING

In this section, we give a mathematical formulation of the HTS tuning problem. Then we detail the heuristic to find Hierarchical Traffic Shaping parameters which minimize bandwidth utilization in the AFDX while ensuring messages schedulability. Finally, some numerical results are illustrated for the same example described in Tables I andII.

A. Problem Formulation

To perform resource savings on the AFDX backbone and enhance margins for future function additions, an adapted optimization process is required to define the best HTS structure within RDC device. The bandwidth utilization in the AFDX induced by the RDC device is considered as a relevant metric to assess the resource saving margins in the AFDX network. Our objective is to find the best HTS structure, i.e. the number and parameters of inner shapers, which minimizes as much as possible the bandwidth utilization in the AFDX while guaranteeing the temporal constraints of upstream and downstream flows. The corresponding optimization problem is formulated as follows:

minimize Shinner Bw(V L(Sh inner )) = vi∈V L(Shinner) L max (v i ) BAG(v i ) subject to ∀m ∈ S up ∪ S down , d CAN (m) + d RDC (m) ≤ Dl m -max m (d AF DX (m)) (8)
where,

• Bw(V L(Sh inner )) is the reserved bandwidth for upstream flows on the AFDX backbone; and it is equal to the sum of AFDX VLs rates depending on the parameters of inner shapers in Sh inner ;

• the constraint corresponds to the schedulability test of upstream and downstream flows. To solve this problem, we introduce in the next section an adequate heuristic approach to find the best HTS configuration which minimizes the objective function and respects the constraints.

B. HTS Heuristic Approach

The Figure 11 illustrates the proposed heuristic to find the optimal configuration of HTS. This heuristic will be processed only in the case where the basic RDC device or the optimized RDC device implementing only MSP strategy leads to a schedulable configuration of upstream and downstream flows. We are not looking through this heuristic to improve the The different steps of this heuristic are as follows:

1) Initialization: First, the heuristic sorts downstream messages set S down in non-decreasing order of periods. At this step, the set of inner shapers is empty, Sh inner = ∅. The heuristic will start by allocating the first message in S down . 2) Iterative construction of inner shapers: Then, the set Sh inner is built iteratively. At the beginning, the first message in S down is inserted in a new shaper sh that would be added to the list of HTS configurations List 0 Shinner . Then, for the next selected message in S down , the heuristic is conducted as follows for each iteration k ≥ 1:

• (a)

C. Numerical Results

To illustrate the heuristic efficiency to find the optimal HTS structure which respects flows temporal constraints, we consider the same example described in Tables I and II. The optimal HTS structure consists of 7 inner shapers having the same period equal to 4ms and the associated downstream flows subsets are as following: This HTS configuration guarantees the schedulability of downstream flows as shown in Figure 12, unlike the one considered in the previous section. Furthermore, it reduces bandwidth utilization in the AFDX when using the optimized RDC device implementing frame packing and HTS algorithm, compared to the optimized RDC device implementingonly frame packing as illustrated in Table IV. However, as it can be noticed, there is a small difference in terms of bandwidth utilization in the AFDX compared to the results obtained in Table III due to the schedulability constraints.

Sh 1 : {m 1 , m 2 }, Sh 2 : {m 3 , m 4 }, Sh 3 : {m 5 , m 6 },
!" !$ !%" !%$ !&" !&$ !*" % & * ) $ ' N ( O %" %% %& %* %) %$ %' %N %( %O &" &% && &* &) 0AM>S-HC1!D64F
;I44?JI!P--I?C@93ID64F B2!Q>L 098R!Q>L Fig. 12. WCRT of downstream flows on CAN VI. AVIONIC CASE STUDY In this section, we validate the efficiency of the optimized RDC device implementing frame packing and HTS algorithm to reduce bandwidth utilization in the AFDX while guaranteeing the upstream and downstream schedulability for a realistic avionic case study.

A. Description

Our case study is a representative avionic communication architecture based on a backbone network AFDX interconnected to one I/O CAN data bus via the optimized RDC device, as shown in Figure 13. The maximum delay bound on AFDX network considered herein is equal to 1.5ms and the CAN load is varied from 6% to 54%. Upstream and downstream flows are randomly generated with a payload of 8bytes and periods ranging in {8, 16, 32, 64, 128}ms. The generated CAN load due to Upstream flows is equal to the one due to downstream flows. For example, when we consider a CAN load of 6% this means that we have 3% due to upstream flows and 3% due to downstream flows. Results illustrated in Figure 14 show the bandwidth utilization in the AFDX induced by upstream flows when using: a basic RDC device with (1:1) strategy, an optimized RDC device implementing only MSP strategy and an optimized RDC device implementing MSP strategy and an optimal HTS structure, i.e., the one obtained with the heuristic described in Section V-B.

As can be noticed, under low CAN loads (up to 30%), the two optimized RDC device configurations induce the same bandwidth utilization in the AFDX which is lower than the utilization obtained with the basic RDC device. These results validate the previous results proved in [START_REF]Interconnection optimization for multi-cluster avionics networks[END_REF] where the MSP strategy offers a significant amelioration of bandwidth utilization in the AFDX, compared to the (1:1) strategy (up to 30% of reduction). However, in this case the HTS algorithm is useless for improving performances.

Under high CAN load (more than 36% and up to 54%), the optimized RDC device implementing MSP strategy and an optimal HTS structure shows significant enhancements in terms of bandwidth utilization in the AFDX, compared to the two first RDC device configurations. For example, under CAN load equal to 54%, we have a reduction of 50%. This fact validates the efficiency of HTS algorithm to guarantee a bandwidth isolation between upstream and downstream flows on CAN, and consequently minimizing WCRTs of upstream flows on CAN. This reduction is in favor of performing MSP strategy within RDC device and consequently reducing the bandwidth utilization in the AFDX.

VII. CONCLUSION

Since resource saving is inherently important to guarantee an easy incremental design process for avionics applications, the design of an optimized RDC device is proposed to interconnect an AFDX backbone to I/O CAN buses.

The optimized RDC device consists of: (i) accurate frame packing unit to manage upstream flows to reduce communication overheads, and consequently to minimize bandwidth utilization in the AFDX; (ii) Hierarchical Traffic Shaping (HTS) algorithm to control downstream flows, and consequently to minimize interferences and to guarantee bandwidth isolation on CAN bus; (iii) support of multiple I/O networks using partitioning to provide the required safety level, i.e., ensuring that an errant I/O network running in one partition will not affect the others.

First, modeling such RDC devices and timing analysis of upstream and downstream flows integrating the effects of frame packing and HTS were detailed. Then, the tuning process of HTS parameters, based on a heuristic approach, to minimize as much as possible bandwidth utilization in the AFDX and to guarantee at the same time upstream and downstream flows requirements was proposed. Finally, the validation of the optimized RDC device was conducted and the performance analysis highlighted its capabilities to improve resource savings for avionic networks, and particularly the use of the HTS algorithm.

The next step in our work consists in analyzing the adaptability of the proposed concepts to the specificities of other I/O data buses like MIL-STD-1553 [START_REF] Incorporated | MIL-STD-1553 Designer guide[END_REF] and TTP/C [START_REF] Kopetz | Event-Triggered Versus Time-Triggered Real-Time Systems[END_REF].

Fig. 1 .

 1 Fig. 1. Multi-cluster avionic communication architecture

Fig. 2 .Fig. 3 .

 23 Fig. 2. Bandwidth Utilization in the AFDX with shared I/O network

Fig. 4 .

 4 Fig. 4. RDC Architectural Overview

Fig. 5 .

 5 Fig. 5. MSP Packing Strategy Process

Fig. 6 .

 6 Fig. 6. Frame unpacking process

Fig. 7 .

 7 Fig. 7. Hierarchical Traffic Shaping Structure

Fig. 9 .

 9 Fig. 9. WCRTs of upstream flows on CAN

Fig. 11 .

 11 Fig. 11. Example of The Heuristic Approach

  we add the selected message to each inner shaper in each HTS configuration in List k-1 Shinner and we build a new configuration by adding a new inner shaper containing only the selected message. Then, we update the inner shaper characteristics of each HTS configuration as defined in Section III-C. Furthermore, for each HTS configuration, we verify the schedulability condition of each upstream flow in S up and of each selected downstream flow. Only feasible configurations if any are considered to form the list List k Shinner and then go to step (b) until the stop condition is verified, i.e. each message in S down has an associated inner shaper in the final HTS configuration. For k ≥ 2 If there is no feasible configuration, go to step (c).• (b) for each configuration of inner shapers in the listList k Shinner , we compute the WCRTs of upstream flows on CAN. Then, we sort the list List k Shinner in non-decreasing order of associated WCRTs ob-tained for upstream flows. Then, we select the first inner shaper configuration Sh inner in the sorted list List k Shinner and we come back to step (a) by considering List k-1 Shinner = Sh inner for the next selected message in S down .• (c) for each inner shaper configuration in List k-1 Shinner , we compute the WCRTs of upstream flows on CAN. Then, we sort the list List k-1 Shinner in non-decreasing order of associated WCRTs obtained for upstream flows. Then, we select the next inner shaper configuration Sh inner in the sorted list List k-1Shinner and we come back to step (a) by considering List k-1 Shinner = Sh inner for the next selected message in S down .

Sh 4 :

 4 {m 7 , m 8 }, Sh 5 : {m 9 , m 10 , m 11 , m 12 }, Sh 6 : {m 13 , m 14 , m 15 , m 16 }, Sh 7 : {m 17 , m 18 , m 19 , m 20 , m 21 , m 22 , m 23 , m 24 }.

Fig. 13 .

 13 Fig. 13. Avionic case study

Fig. 14 .

 14 Fig. 14. Bandwidth Utilization in the AFDX with optimal HTS structure


Open Archive TOULOUSE Archive Ouverte (OATAO)

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Any correspondance concerning this service should be sent to the repository administrator:

Inverse problems in hydraulics are still open questions such as the estimation of river discharges. Remotely sensed measurements of hydrosystems can provide valuable information but adequate methods are still required to exploit it. The future Surface Water and Ocean Topography (SWOT) mission would provide new cartographic measurements of inland water surfaces. The highlight of SWOT will be its almost global coverage and temporal revisits on the order of 1 to 4 times per 22 days repeat cycle [START_REF] Rodriguez | SWOT science requirements document[END_REF]. Lots of studies have shown the possibility of retrieving discharge given the river bathymetry or roughness and/or in situ time series. The new challenge is to use SWOT type data to inverse the triplet formed by the roughness, the bathymetry and the discharge. The method presented here is composed of two steps: following an inverse formulation from [START_REF] Gessese | Bathymetry reconstruction based on the zero-inertia shallow water approximation[END_REF], the first step consists in retrieving an equivalent bathymetry profile of a river given one in situ depth measurement and SWOT like data of the water surface, that is to say water elevation, free surface slope and width. From this equivalent bathymetry, the second step consists in solving mass and Manning equation in the least square sense [START_REF] Garambois | Inference of river properties from remotly sensed observations of water surface, under final redaction for HESS[END_REF]. Nevertheless, for cases where no in situ measurement of water depth is available, it is still possible to solve a system formed by mass and Manning equations in the least square sense (or with other methods such as Bayesian ones, see e.g. [START_REF] Durand | Sacramento river airswot discharge estimation scenario[END_REF]). We show that a good a priori knowledge of bathymetry and roughness is compulsory for such methods. Depending on this a priori knowledge, the inversion of the triplet (roughness, bathymetry, discharge) in SWOT context was evaluated on the Garonne River [START_REF] Garambois | Garonne River discharge estimation[END_REF][START_REF] Garambois | Sensitivity of discharge uncertainty to measurement errors, case of the Garonne River[END_REF]. The results are presented on 80 km of the Garonne River downstream of Toulouse in France [START_REF] Roux | Tests of reach averaging and manning equation on the Garonne River[END_REF]. An equivalent bathymetry is retrieved with less than 10% relative error with SWOT like observations. After that, encouraging results are obtained with less than 10% relative error on the identified discharge.

  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 11376

	To cite this version : Garambois, Pierre-André and Monnier, Jérôme
	and Roux, Hélène Inferring river properties with SWOT like data.
	(2014) In: European Geosciences Union General Assembly 2014, 27
	April 2014 -02 May 2014 (Vienna, Austria).

Pierre-André GARAMBOIS (1), Jérôme MONNIER (1), and Hélène ROUX[START_REF] Gessese | Bathymetry reconstruction based on the zero-inertia shallow water approximation[END_REF] (1) Université de Toulouse, Institut de Mathématiques de Toulouse (IMT), France (p.garambois@gmail.com), (2) Université de Toulouse, Institut de Mécanique des fluides de Toulouse (IMFT), France


Audrey Douinot
email: audrey.douinot@imft.fr

Hélène Roux

Pierre-André Garambois

Kevin Larnier

Impact of rainfall spatial variability on Flash Flood Forecasting

According to the United States National Hazard Statistics database, flooding and flash flooding have caused the largest number of deaths of any weather-related phenomenon over the last 30 years (Flash Flood Guidance Improvement Team, 2003). Like the storms that cause them, flash floods are very variable and non-linear phenomena in time and space, with the result that understanding and anticipating flash flood genesis is far from straightforward. In the U.S., the Flash Flood Guidance (FFG) estimates the average number of inches of rainfall for given durations required to produce flash flooding in the indicated county. In Europe, flash flood often occurred on small catchments (approximately 100 km2) and it has been shown that the spatial variability of rainfall has a great impact on the catchment response (Le Lay and Saulnier, 2007). Therefore, in this study, based on the Flash flood Guidance method, rainfall spatial variability information is introduced in the threshold estimation. As for FFG, the threshold is the number of millimeters of rainfall required to produce a discharge higher than the discharge corresponding to the first level (yellow) warning of the French flood warning service (SCHAPI: Service Central d'Hydrométéorologie et d'Appui à la Prévision des Inondations). The indexes δ1 and δ2 of Zoccatelli et al. ( 2010), based on the spatial moments of catchment rainfall, are used to characterize the rainfall spatial distribution. Rainfall spatial variability impacts on warning threshold and on hydrological processes are then studied. The spatially distributed hydrological model MARINE (Roux et al., 2011), dedicated to flash flood prediction is forced with synthetic rainfall patterns of different spatial distributions. This allows the determination of a warning threshold diagram: knowing the spatial distribution of the rainfall forecast and therefore the 2 indexes δ1 and δ2, the threshold value is read on the diagram. A warning threshold diagram is built for each studied catchment. The proposed methodology is applied on three Mediterranean catchments often submitted to flash floods. The new forecasting method as well as the Flash Flood Guidance method (uniform rainfall threshold) are tested on 25 flash floods events that had occurred on those catchments. Results show a significant impact of rainfall spatial variability. Indeed, it appears that the uniform rainfall threshold (FFG threshold) always overestimates the observed rainfall threshold. The difference between the FFG threshold and the proposed threshold ranges from 8% to 30%. The proposed methodology allows the calculation of a threshold more representative of the observed one. However, results strongly depend on the related event duration and on the catchment properties. For instance, the impact of the rainfall spatial variability seems to be correlated with the catchment size. According to these results, it seems to be interesting to introduce information on the catchment properties in the threshold calculation. NHESS, 11(9), 2567-2582. Zoccatelli, D., Borga, M., Zanon, F., Antonescu, B. and Stancalie, G., 2010. Which rainfall spatial information for flash flood response modelling? A numerical investigation based on data from the Carpathian range, Romania. Journal of Hydrology, 394(1-2), 148-161.

Flash

  Flood Guidance Improvement Team, 2003. River Forecast Center (RFC) Development Management Team. Final Report. Office of Hydrologic Development (OHD), Silver Spring, Mary-land. Le Lay, M. and Saulnier, G.-M., 2007. Exploring the signature of climate and landscape spatial variabilities in flash flood events: Case of the 8-9 September 2002 Cévennes-Vivarais catastrophic event. Geophysical Research Letters, 34(L13401), doi:10.1029/2007GL029746. Roux, H., Labat, D., Garambois, P.-A., Maubourguet, M.-M., Chorda, J. and Dartus, D., 2011. A physically-based parsimonious hydrological model for flash floods in Mediterranean catchments. Nat. Hazards Earth Syst. Sci. J1 -


Aude Beauger
email: aude.beauger@uca.fr

Carlos E Wetzel

Olivier Voldoire

Elisabeth Allain

Vincent Breton

Didier Miallier

Luc Ector

Fontina gen. nov. (Bacillariophyta): a new diatom genus from a thermo-mineral spring of the French Massif Central (France)

Keywords: Fontina arverna, mineral springs, new genus, raphid diatom, taxonomy

Light and scanning electron microscope observations on the genus Fontina gen. nov. from a thermo-mineral spring of the Massif Central (France) are presented. Based on morphology, the new genus shows features that have not been described previously, such as the stria pattern, interrupted at the valve face/mantle junction and composed of one long, slit-like areola on both valve face and mantle. Externally, areolae are closed by hymenes. Fontina arverna sp. nov. is described as the typus generis of Fontina. This new genus was compared with some similar freshwater genera such as Adlafia, Chamaepinnularia, Genkalia, Germainiella, Microfissurata and Nupela. So far, we are unable to establish an evolutionary link or cladistic association with currently known genera. The new genus is described from a sampling site characterized by high conductivity and high carbonate concentration, brackish conditions and whose water originates deep in the crust (high lithium concentration).

Introduction

Mineral and thermal springs are formed by hydro-geological processes, linked to volcanic and tectonic activities. A significant portion of rain water feeds shallow aquifers, while elsewhere it slowly infiltrates faults up to several kilometers deep. Indeed, mineral springs coincide with the fault zones [START_REF] Risler | Description et classification géologique des sources minérales et thermales du Massif Central[END_REF]. It is well known that "fracturing the platform promotes the circulation of fluids (water and gas) including those of carbon dioxide (CO2) and helium (He), which may be hampered by the presence of clay or marl" [START_REF] Gal | What can be learned from natural analogue studies in view of CO2 leakage issues in Carbon Capture and Storage applications? Geochemical case study of Sainte-Marguerite area (French Massif Central)[END_REF]. The rainwater infiltrates the soil by gravity and capillarity to the hydrostatic level, then rises through hydrostatic or gaseous pressure. At several kilometers deep, warming promotes progressive destruction by hydrolysis of minerals such as feldspar rocks, through which constituents such as sodium, calcium and potassium come into solution. Before reaching the surface where the fractures have a tree-like aspect, water can be mixed, in varying proportions, with the surface water layers (Labernardière, personal communication). It is during this journey that they acquire their different characteristics [START_REF] Risler | Description et classification géologique des sources minérales et thermales du Massif Central[END_REF]. Thus, mineral and thermal springs present waters characterized by their gaseous properties, with significant mineralization and sometimes high temperatures.

Depending on their abiotic properties, different ecosystems may develop. Some springs create inland saline areas under the influence of saline waters that accompany the salt deposits, or as areas exposed to water deficit in dry climates [START_REF] Reimold R | Ecology of halophytes[END_REF][START_REF] Poljakoff-Mayber | Plants in Saline Environments[END_REF]. These environments are relatively widespread throughout the world and cover ca. 10% of the land [START_REF] Glenn | Halophytes as resource for livestock and rehabilitation of degraded lands[END_REF][START_REF] Piernik | Ecological Pattern of Inland Salt Marsh Vegetation in Central Europe[END_REF]). Inland salt environments occur in limited areas, mostly on "fossil salt deposits and around salty springs" [START_REF] Piernik | Ecological Pattern of Inland Salt Marsh Vegetation in Central Europe[END_REF]. Other springs containing carbonates can induce the formation of travertine, i.e. a limestone rock, and are known as Limestone-Precipitating Springs (LPS) [START_REF] Cantonati | A global review on ambient Limestone-Precipitating Springs (LPS): Hydrogeological setting, ecology, and conservation[END_REF]. Depending on the geology, some springs can be both LPS and salty. Springs have been studied by diatomists all over the world, often leading to the discovery of new taxa [START_REF] Werum | Diatoms in springs, from Central Europe and elsewhere under the influence of hydrogeology and anthropogenic impacts[END_REF][START_REF] Cantonati | Achnanthidium dolomiticum sp. nov. (Bacillariophyta) from oligotrophic mountain springs and lakes fed by dolomite aquifers[END_REF][START_REF]Diatom flora in springs of Łódź Hills (Central Poland). Biodiversity, taxonomy, and temporal changes of epipsammic diatom assemblages in springs affected by human impact[END_REF][START_REF] Reichardt E | Bemerkenswerte Diatomeenfunde aus Bayern V 1 -Neue und seltene Arten aus der Schwarzachklamm[END_REF][START_REF]Nupela marvanii sp. nov., and N. lapidosa (Krasske) Lange-Bertalot in Poland with notes on the distribution and ecology of the genus Nupela (Bacillariophyta)[END_REF][START_REF]Species composition and distribution of diatom assemblages in spring waters from various geological formations in southern Poland[END_REF][START_REF]Diatom flora in springs of Łódź Hills (Central Poland). Biodiversity, taxonomy, and temporal changes of epipsammic diatom assemblages in springs affected by human impact[END_REF][START_REF] Lai | Sellaphora gologonica sp. nov. (Bacillariophyta, Sellaphoraceae), a new diatom species from a Mediterranean karst spring (Sardinia, Italy)[END_REF].

The French Massif Central (over 85,000 km²) is composed of mountain reliefs, plateaus and volcanoes (quiescent), where the Hercynian platform appears at the surface, surrounded by different sedimentary basins. It is well known that the many faults in the massif allow the circulation of water in the rocks and the emergence of water after a more or less long travel across the earth's crust. Thus, in the French Massif Central, and more precisely in the Puy-de-Dôme department, Truchot (1878) described more than 200 springs.

Due to the history of the massif, a high variety of habitat conditions are present, including high altitude springs (>1000 m a.s.l.) but also the hottest spring in Europe (80 °C). Previous studies conducted on springs from the Massif Central have revealed the high algal biodiversity (Héribaud 1893[START_REF] Heribaud | Les diatomées des travertins d'Auvergne[END_REF][START_REF] Chaouite | La flore diatomique des eaux minérales de Vichy (Allier) et de Chaudes-Aigues (Cantal)[END_REF][START_REF] Tudesque | Etude hydrobiologique de trois sites halophiles: Bard, Saint Nectaire[END_REF][START_REF] Cordonnier | Les sources salées d'Auvergne[END_REF][START_REF] Beauger | Two new Navicula species (Bacillariophyceae) from Western Europe[END_REF], 2016, 2017[START_REF] Beauger | Pseudostaurosira bardii (Fragilariaceae, Bacillariophyta), a new species from a saline hydrothermal spring of the Massif Central (France)[END_REF].

During a biodiversity survey of mineral springs around the city of Saint-Nectaire, a new genus was observed in one of them. This paper describes the new genus and species, Fontina arverna, using light (LM) and scanning electron microscopy (SEM). Based on the available literature, a morphological comparison is made with the most similar genera and together with information on their ecology.

Material and methods

In summer 2016, a survey was performed around the former thermal city of Saint-Nectaire.

The granitic horst of Saint-Nectaire, flanked on the east and west by two Oligocene compartments and divided by N.S. and E.W. faults, is closely related to the Limagne fracture system [START_REF] Risler | Description et classification géologique des sources minérales et thermales du Massif Central[END_REF]. More than 40 springs were listed by [START_REF] Truchot | Dictionnaire des eaux minérales du département du Puy-de-Dôme[END_REF] emerging from this granitic context. Currently, some springs are used for petrification craft industry due to the hardness of the water. The sample was collected in the thermal (32.2 °C) and carbonate (3240 mg L -1 ) spring (according to the classification of Glazier 2014) of Antonia in Saint-Nectaire (French Massif Central) (Fig. 1). Due to their former therapeutic use, many springs were modified by drilling to increase their discharge. It was the case for the Antonia spring. Thus, the actual outlet is a former borehole dug in 1980. The spring has a low radium content (0.7 millimicrocurie, [START_REF] Jacquet | Contribution à l'étude de la radioactivité des eaux minérales et du magnétisme des roches volcaniques du département du Puy-de-Dôme[END_REF].

The diatoms were sampled on travertine, a sedimentary rock by brushing the stone.

The geographical position of the sampling site was taken using a DGPS Trimble Geo7x, in Lambert 93. Samples were cleaned using hydrogen peroxide (H2O2, 35%) and hydrochloric acid (HCl), and rinsed several times. Cleaned material was diluted with distilled water to avoid excessive concentrations of diatom valves on the slides and mounted in Naphrax®. LM and morphometric measurements were performed using a Leica® DMRX bright field microscope with 100x oil immersion objective, and light photographs were taken with a Leica® DC500 camera. For scanning electron microscopy (SEM), parts of the oxidized suspensions were filtered and filters were mounted on aluminium stubs and coated with platinum. An ultrahigh-resolution analytical field emission (FE) scanning electron microscope Hitachi SU-70 (Hitachi High-Technologies Corporation, Japan) operated at 5 kV and 10 mm distance was used for the analysis. SEM images were taken using the lower (SE-L) and upper (SE-U) detector signal and sometimes tilted up to an angle of 28 degrees. Conductivity (μS.cm -1 ), pH (pH units), and water temperature (°C) were measured at the sampling site, using a WTW Multiline P4. The oxygen was measured using an oximeter Ysi ProODO. A water sample was collected for further chemical analysis in the laboratory and was analysed using the high-pressure ion chromatography technic.

Spring water radioactivity (radon) was measured using gamma-spectrometry with a well Germanium detector and a gamma survey was conducted at spring site using a Myrion Colibri VLD instrument. 37), one on the valve face and the other on the mantle. Depending on the valve shape, the valve face areola is sometimes shorter than the one on the mantle (Fig. 28), which is relatively deep. Moreover, the lengths of the areolae, decreasing from the apex to the central area, are not the same on each side of the valve face, emphasising the asymmetry of the frustule. Internally, the virgae can sometimes be bifurcated near the valve face/mantle junction, randomly along the valve (usually near the valve centre).

Results

Fontina

The areolae are closed externally by hymenes and internally are composed of small pores that are difficult to observe (Fig. 38). Externally, the proximal raphe endings are straight, slightly expanded, or pore-like and slightly deflected to the same side (Figs 21-34) while internally, they are expanded and slightly deflected to the same side . Distal endings of raphe externally slightly deflected and reaching the valve mantle at the apex. Both endings are deflected to the same side . Internally, the distal raphe fissures end in small raised helictoglossae 39). Girdle bands appeared perforated at the apex with two rows of areolae near the valve apices (Fig. 39).

Holotype. Deposited in

Physical and chemical variables:

The conductivity of this thermo-mineral spring is high with mainly bicarbonates, chlorides and sodium (Table 1). The concentration in dissolved oxygen is low and the lack of anthropogenic impact is revealed by the concentrations of nitrates, nitrites and phosphates. The concentration of lithium and bromine (respectively 14.1 and 5.2 mg L -1 ) underline the deep origin of the water and its circulation through the granite [START_REF] Michard | Behaviour of major elements and some trace elements (Li, Rb, Cs, Sr, Fe, Mn, W, F) in deep hot waters from granitic areas[END_REF]). Spring water radioactivity was measured resulting in radon activity of 11.3 +/-0.2 Bq/l. It appears that the dissolved radium content has been ignored for this estimate. Gamma, dose rates up to 1100 nSv/h, have been measured on top of the travertine where diatoms were sampled, revealing significant but low radioactivity in the sediment.

Discussion

The precise taxonomic position of this taxon is unclear. The ultrastructural analysis revealed that its combination of morphological characters made it difficult to establish relationships with currently described diatom genera, although it probably belongs in the family Naviculaceae.

Fontina is characterized by the peculiar stria ultrastructure and valve asymmetry. The most similar genus to Fontina is Nupela (Table 2) as both taxa can be asymmetric, without a conopeum and striae that cannot be resolved with LM. However, they differ in several morphological features. Thus, while the striae of Fontina are briefly interrupted near the valve face/mantle junction, continuing onto the mantle with only a single slit-like areola on the valve face, Nupela is characterized by many elliptical slit-like areolae per stria [START_REF] Vyverman | Nupela giluwensis gen. & spec. nov. a new genus of naviculoid diatoms[END_REF][START_REF] Siver | Notes on the genus Nupela (Bacillariophyceae) including the description of a new species, Nupela scissura sp. nov. and an expanded description of Nupela paludigena[END_REF][START_REF] Sala | Nupela species (Naviculales: Bacillariophyceae) from Colombian lowland waters including N. acaciensis nov. sp. and N. catatumbensis nov. sp[END_REF][START_REF] Miscoe | I. Investigation of the cave diatom flora of Kauai, Hawaii: an emphasis on taxonomy and distribution[END_REF]). The areolae in Nupela are covered internally by hymenes perforated at the centre; some species also have external hymenate areola occlusions. While the external distal raphe endings of Fontina are slightly deflected, those of Nupela are sharply curved. The internal proximal raphe endings of Nupela can be T-shaped or hook-shaped. The girdle bands of Fontina are perforated near the apex which is not the case for Nupela. Finally, Nupela is widespread and present in freshwater environments with low conductivity and in aerial habitats [START_REF] Vyverman | Nupela giluwensis gen. & spec. nov. a new genus of naviculoid diatoms[END_REF][START_REF] Siver | Notes on the genus Nupela (Bacillariophyceae) including the description of a new species, Nupela scissura sp. nov. and an expanded description of Nupela paludigena[END_REF][START_REF] Spaulding | Nupela. In: Diatoms of the United States[END_REF][START_REF] Kulikovskiy | Nupela matrioschka sp. nov., Nupela thurstonensis comb. nov. and Nupela neogracillima comb. & nom. nov. (Bacillariophyceae): critical analysis of their morphology[END_REF][START_REF] Sala | Nupela species (Naviculales: Bacillariophyceae) from Colombian lowland waters including N. acaciensis nov. sp. and N. catatumbensis nov. sp[END_REF][START_REF] Falasco | Nupela troglophila sp. nov., an aerophilous diatom (Bacillariophyta) from the Bossea cave (NW Italy), with notes on its ecology[END_REF][START_REF] Miscoe | I. Investigation of the cave diatom flora of Kauai, Hawaii: an emphasis on taxonomy and distribution[END_REF].

Adlafia (Table 2) has similar features to Fontina, including the presence of external hymenes on areolae, the absence of a conopeum, and perforated girdle bands, but it differs in the striation pattern [START_REF] Moser | Insel der Endemiten. Geobotanisches Phänomen Neukaledonien [Island of endemics. New Caledonia -a geobotanical phenomenon[END_REF][START_REF] Morales | A new species of the diatom genus Adlafia (Bacillariophyceae) from the United States[END_REF][START_REF] Liu | Adlafia sinensis sp. nov. (Bacillariophyceae) from the Wuling Mountains Area, China, with reference to the structure of its girdle bands[END_REF]. In Adlafia striation is very dense, composed of very fine, radiate striae, resolvable with LM whereas Chamaepinnularia has areolae closed by hymenes, a conopeum is absent and girdle bands are also perforated as in Fontina. This genus has symmetric valves that are usually linear-elliptic, linear-lanceolate, elliptic-lanceolate or undulate [START_REF] Lange-Bertalot | Oligotrophie-Indikatoren. 800 Taxa repräsentativ für drei diverse Seen-Typen. Kalkreich -Oligodystroph -Schwach gepuffertes Weichwasser [Indicators of oligotrophy. 800 taxa representative of three ecologically distinct lake types. Carbonate buffered -Oligodystrophic -Weakly buffered soft water[END_REF], Cantonati & Lange-Bertalot 2009[START_REF] Wetzel | New combinations and type analysis of Chamaepinnularia species (Bacillariophyceae) from aerial habitats[END_REF]. The striae are composed of upto three slit-like areolae and are irregularly subdivided by silica bridges, a characteristic never encountered in Fontina. Striae can also consist of two pores, one small and rounded at the valve face/mantle junction, with the other, elongated and located on the valve face [START_REF] Wetzel | New combinations and type analysis of Chamaepinnularia species (Bacillariophyceae) from aerial habitats[END_REF]). The internal proximal raphe endings and the external distal raphe endings are unilaterally hooked and bent to the same side respectively, whereas they are slightly deflected to the same side for the new genus. Chamaepinnularia is widespread and inhabits mainly lowconductivity water, although Chamaepinnularia plinskii Żelazna-Wieczorek & Olszyński occurs in high-conductivity water. Chamaepinnularia species have been observed in fresh-to marine environments and in thermal springs, e.g. Chamaepinnularia thermophila (Manguin)

C.E. Wetzel & Ector (Lange-Bertalot & Metzeltin 1996, Cantonati & Lange-Bertalot 2009[START_REF] Wetzel | New combinations and type analysis of Chamaepinnularia species (Bacillariophyceae) from aerial habitats[END_REF], Wetzel & Ector 2016[START_REF] Żelazna-Wieczorek | Taxonomic revision of Chamaepinnularia krookiformis Lange-Bertalot et Krammer with a description of Chamaepinnularia plinskii sp[END_REF].

Genkalia has isopolar valves and asymmetric individuals are currently unknown.

Valves are elliptical to linear-elliptical or linear-lanceolate with mainly rounded ends, except Genkalia subrostrata (Skvortzow) Kulikovskiy, Lange-Bertalot & Metzeltin which has moderately protracted ends [START_REF] Kulikovskiy | Lake Baikal: Hotspot of endemic diatoms I[END_REF][START_REF] Wojtal | Diversity of the genus Genkalia (Bacillariophyta) in boreal and mountain lakes -taxonomy, distribution and ecology[END_REF]). The internal proximal raphe endings are shortly bent to the primary side and not deflected. The external distal raphe endings are strongly bent to the secondary side and extend to the smooth junction between valve face and mantle [START_REF] Kulikovskiy | Lake Baikal: Hotspot of endemic diatoms I[END_REF]. Striae are composed of a large number of round, elliptic or transapically elongated areolae unlike in Fontina with one slitlike areola on the valve face and another on the mantle. Genkalia species are observed in lakes, except for Genkalia subprocera that was described in a spring, from calcium-rich water and high mineral content [START_REF] Hustedt F | Diatomeen aus Seen und Quellgebieten der Balkan-Halbinsel[END_REF][START_REF] Wojtal | Diversity of the genus Genkalia (Bacillariophyta) in boreal and mountain lakes -taxonomy, distribution and ecology[END_REF].

Germainiella differs in several morphological features from Fontina [START_REF] Metzeltin | Diatoms of Uruguay. Compared with other taxa from South America and elsewhere[END_REF], Le Cohu et al. 2016). Valves are linear to narrowly lanceolate in shape, symmetric with capitate to subcapitate apices for Germainiella while for Fontina, they are slightly asymmetric, elliptical with rounded, capitate or cuneate apices.Unlike Fontina, Germainiella has a conopeum covering both the valve face and part of the mantle. Even though valve appears hyaline and the striae are composed of one slit-like areola, the presence of the conopeum allows separation from Fontina. In addition, hymenes are not observed in Germainiella. The external distal raphe endings are hooked for Germainiella but slightly deflected for Fontina.

Microfissurata has lanceolate to linear-elliptical valves with more or less protracted ends, unlike Fontina with narrowly elliptical, linear elliptical, lanceolate elliptical, broadly elliptical valves and broadly rounded to slightly capitate or cuneate ends (Cantonati et al. 2009). Striae are open slits, which are internally completely closed by delicate hymenes, often corroded in prepared valves (Cantonati et al. 2009). The main difference between this genus and Fontina is the presence of an axial area that is wide or very wide, especially the central area in Microfissurata. This central area is an "apically rather expanded fascia" (Cantonati et al. 2009), a characteristic never encountered in Fontina. Moreover, the two known species of Microfissurata are encountered in freshwater and intermittently wet habitats characterized by low conductivity, contrary to Fontina from a thermo-mineral spring of high conductivity.

Microfissurata also appears to be mostly epiphytic, growing on bryophytes (Cantonati et al. 2009) unlike Fontina that is epilithic.

In conclusion, this study of the diatom community of a thermo-mineral spring revealed a small, slightly asymmetric taxon with a previously unknown combination of the morphological characters. The new species has a unique pattern of characteristics which precludes allocation to any known genus, hence our description of Fontina. 14.9 Oxygen (mg L -1 )

1.1 Li + (mg L -1 ) 14.1 Na + (mg L -1 ) 2049.6 NH 4 + (mg L -1 ) 2.6 K + (mg L -1 ) 218.8 Mg 2+ (mg L -1 ) 103.0 Ca 2+ (mg L -1 ) 26.9 F -(mg L -1 ) 0.9 Cl -(mg L -1 ) 2195.4 NO 2 -(mg L -1 ) 0.0 NO 3 -(mg L -1 ) 0.4 PO 4 3-(mg L -1 ) 0.1 Br (mg L -1 ) 5.2 SO 4 2-(mg L -1 ) 121.0 HCO 3 -(mg L -1 ) 3240.0

  Beauger, C.E. Wetzel & Ector gen. nov. Description: it is a small-celled diatom. No girdle views were observed. Valves are from narrowly elliptical, linear-elliptical, lanceolate-elliptical to broadly elliptical with endings broadly rounded to slightly capitate or cuneate. The valve face appears hyaline with any structure other than the raphe and the axial area. Valves are slightly asymmetric to the apical axis. Under SEM, the axial area is narrow and enlarged near the central area. Striae are interrupted at the valve face/mantle junction and composed of one long, slit-like areola on both valve face and mantle. Externally, areolae are closed by hymenes. External distal raphe fissures are slightly deflected to the same side and internally, they end in small raised helictoglossa. Girdle bands are perforated. Generitype: Fontina arverna Beauger, C.E. Wetzel & Ector sp. nov. (Figs 2-34) The term Fontina refers to the Latin word "Fons"= spring, the habitat where the new genus was observed. Fontina arverna Beauger, C.E. Wetzel & Ector sp. nov. (Figs 2-39) Description: Length 3.5-14 μm, breadth 1.5-3.5 μm, stria density 60-70 in 10 μm. LM: Raphe filiform conspicuous. Valves appear hyaline and are slightly transapically curved. The axial area is narrow. SEM: The axial area is narrow and enlarged near the central area. Thin striae are interrupted near the valve face/mantle junction, continuing onto the mantle (Figs 21-39). Valve face striae are composed of elongated areolae (Figs 35-

  Herbiers Universitaires de Clermont-Ferrand, France (CLF 104889), shown here in Figs 2-20 (LM) and 21-39 (SEM). Isotypes. Deposited in Herbiers Universitaires de Clermont-Ferrand, France (CLF 104890) and in Botanic Garden Meise, Belgium (BR-4517). Type locality. Saint-Nectaire, Anthonia spring, France (altitude: 691m, E 699358.66, N6498243.64 -Lambert 93). Sample NE10-23072016-AN collected the 23th of July 2016 by A. Beauger. Etymology. The epithet "arverna" refers to the Auvergne region (part of the Massif Central near Saint-Nectaire) and the name of the Gallic people in this part of France. Ecology and associated diatoms species: The type population of F. arverna was found in the Anthonia spring where it represents 14% of the epilithic diatom flora. The dominant taxa were Halamphora coffeaeformis (C. Agardh) Levkov (43%), Navicula sanctamargaritae Beauger in Beauger et al. (26%), Crenotia thermalis (Rabenhorst) Wojtal (9%) and Nitzschia valdecostata Lange-Bertalot & Simonsen (5%).

Table 2

 2 documents other genera that show some similar combinations of morphological features: Adlafia Gerd Moser, Lange-Bertalot & Metzeltin in Lange-Bertalot et al. (1996), Chamaepinnularia Lange-Bertalot & Krammer Metzeltin in Lange-Bertalot & Metzeltin (1996), Genkalia Kulikovskiy, Lange-Bertalot & Metzeltin in Kulikovskiy et al. (2012), Germainiella Lange-Bertalot & Metzeltin in Metzeltin et al. (2005), Microfissurata Lange-Bertalot, Cantonati & Van de Vijver in Cantonati et al. (2009) and Nupela Vyverman & Compère.

Fontina

  valves appear hyaline. Moreover, the valves are symmetric. Adlafia has striae composed of round areolae occluded by a porous vola lying on the outer periphery of each areola unlike Fontina, whose areolae are slit-like and the striae briefly interrupted near the valve face/mantle junction, before continuing onto the mantle. Both genera have areolae occluded by hymenes. The external distal raphe endings of Adlafia are strongly bent and angular, bur slightly deflected in Fontina. The internal proximal raphe endings are expanded and slightly deflected in Fontina, butconspicuously bent in the same direction and opposite to the distal ends in Adlafia. The girdle bands of both genera are perforated; Adlafia has two rows of poroids on the valvocopula (sometimes one row becoming two toward the valve apices;[START_REF] Morales | A new species of the diatom genus Adlafia (Bacillariophyceae) from the United States[END_REF]. Adlafia species live in freshwater ecosystems[START_REF] Moser | Insel der Endemiten. Geobotanisches Phänomen Neukaledonien [Island of endemics. New Caledonia -a geobotanical phenomenon[END_REF][START_REF] Morales | A new species of the diatom genus Adlafia (Bacillariophyceae) from the United States[END_REF][START_REF] Spaulding | Adlafia. In: Diatoms of the United States[END_REF][START_REF] Liu | Adlafia sinensis sp. nov. (Bacillariophyceae) from the Wuling Mountains Area, China, with reference to the structure of its girdle bands[END_REF][START_REF] Van De Vijver B | Michelcostea, a new diatom genus (Bacillariophyta) from the sub-Antarctic Region[END_REF], Marquié et al. 2018).

Figure 1 :

 1 Figure 1: Map of the studied springs. a: map of Europe; b and c: general location map of the French Massif Central (in grey) and of the study area where Anthonia spring is located (square); d: photography of the Anthonia spring.

Figs 2 -

 2 Figs 2-34: Fontina arverna sp. nov. typus generis of Fontina Beauger, C.E. Wetzel & Ector sp. nov., LM. (Figs 2-20). Type population from Anthonia spring. SEM. Figs 21-34. Type population from Anthonia spring. External view of an entire valve showing the raphe structure and the striae. Scale bar = 10 µm (Figs 2-20), 4 µm (Figs 21, 23-26), 3 μm (Figs 22, 27-31), 2 μm (Figs 32-33).

Figs 35- 39 :

 39 Figs 35-39: Fontina arverna sp. nov. typus generis of Fontina Beauger, C.E. Wetzel & Ector sp. nov. SEM. Figs 35-39. Type population from Anthonia spring. Internal view. Figs 35-37, 39. Internal view of an entire valve showing the raphe structure, the striae, the helictoglossa

Table 1 :

 1 Physical and chemical variables measured in the Anthonia spring at Saint-Nectaire on July 23, 2016.

		Anthonia spring
	Conductivity (µS cm -1 )	9520
	pH	7.0
	Temperature (°C)	32.2
	Oxygen (%)

Table 2 :

 2 Comparison of key features among Fontina gen. nov. and similar genera.

	Character	Fontina gen. nov.	Adlafia	Chamaepinnularia	Genkalia	Germainiella	Microfissurata	Nupela
	Valve symmetry	slightly asymmetric	symmetric	symmetric	symmetric	symmetric	symmetric	symmetric or slightly
								asymmetric
	Valve shape	narrowly elliptical,	linear to linear-	linear-elliptical,	elliptic to linear-	linear to narrowly	lanceolate to linear-	narrowly elliptical to
		linear-elliptical,	lanceolate	linear-lanceolate,	elliptic or linear-	lanceolate	elliptical	lanceolate
		lanceolate-elliptical		elliptic-lanceolate	lanceolate
		broadly elliptical		or undulate
	Endings	broadly rounded to	blunt, rostrate, or	rounded or	rounded or	capitate to	more or less protracted	rostrate, capitate or
		slightly capitate or	subcapitate	rostrate	moderately	subcapitate	ends	apiculate
		cuneate			protracted
	Internal	expanded and slightly	conspicuously bent	straight but	shortly bent to the	expanded and	deflected to the same	straight, simple or T-
	proximal raphe	deflected to the same	in the same direction	unilaterally	primary side	slightly deflected	side or even slightly	shaped or hook-shaped
	endings	side	and opposite to the	hooked		to the same side	hooked
			distal ends
	Internal distal	end in small	end in small raised	end in small raised	end in small	end in	end in small,	end in helictoglossa
	raphe endings	helictoglossa	helictoglossa	helictoglossa	raised	helictoglossa	helictoglossa	(sometimes absent)
					helictoglossa
	External	straight, slightly	opposite to the other,	inconspicuous;	proximally not	expanded and	expanded, slightly	inconspicuous or
	proximal raphe	expanded, or pore-	and sometimes	opposite to the	expanded, curving	slightly deflected	deflected to the same	expanded pore-shape
	endings	like and slightly	slightly deflected	other, and	gently to the	to the same side	side
		deflected to the same	toward the same side	sometimes slightly	primary side
		side	and opposite to the	deflected toward
			distal ends	the same side
	External distal	slightly deflected to	strongly bent and	bent to hooked	strongly bent to	hooked and	deflected to the same	sharply curved into one
	raphe endings	the same side and	angular, deflected to	towards the same	the secondary side	reaching the valve	side	side of the valve
		reaching the valve	the same side	direction	extended to the	mantle at the apex
		mantle at the apex			junction between
					valve face and
					mantle
	Striae/alveoli	uniseriate, briefly	striae radial,	composed of slit-	uniseriate,	composed of one	open slits externally	uniseriate, 2 to 6
	structure	interrupted near the	uniseriate, composed	like areolae (up to	uninterrupted	slit-like areola		elliptical slit-like
		valve face/mantle	of round areolae,	three), irregularly	from valve face to			areolae per stria
		junction, continuing	occluded by a porous	subdivided by	mantle, composed
		on the mantle,	vola	silica bridges	of round, elliptic
		composed of two slit-			or transapically
		like areolae, one on			elongated areolae

Acknowledgements

We thank Diba Khan-Bureau (Three Rivers Community College, Norwich, Connecticut, USA) for her precious English corrections and Eduardo A. Morales (Laboratório da Água, Universidade de Évora, Évora, Portugal) for his valuable comments. We also thank Eric Papon and Marion Lefeuvre for their time in the field and for making easier access to the spring. Two anonymous reviewers are thanked for their valuable comments.

Funding

Funding for this research was partly provided in the framework of the project DIATOMS (LIST -Luxembourg Institute of Science and Technology), and by the SIVU Couze Chambon amont, Communauté de communes du Massif du Sancy, and Fontaines Pétrifiantes of Saint-Nectaire.


Objectives

Our project aims at examining wild silkS in two ways:

• 1/ by collecting and geo-localising data on archaeological finds and historical documents in French museum collections and archives -textiles, cocoons, textiles and written commentaries by 19 th -early 20 th century scientific research scientists • 2/ by comparing the past situation with what can be observed today on the same 'living' documents and wild silkS producers and users in Southeast Asia, Japan, India, and West Africa.

Wild Silks in the past and today

Archaeological finds show the long-lasting use in Human industries of various Lepidoptera moths producing silk. Large families as Bombycidae and Saturniidae, and some Lasiocampidea and Notodontidea, considered by silk specialists as producing 'wild silk', have been used worldwide in local textile industries. Specimens, eggs, cocoons, filaments, threads, fabrics, and the techniques to process them, have travelled long distances along the silkS roads. Wild silk tentatively identified as Antherea assamensis, A. mylitta, and maybe Philosamia have been used in the Indus valley (contemporary Pakistan) at least during the second half of the 3 rd millennium BC, while two other species -Pachypasa otus and Saturnia pyriseemed present during the following millennium in the Aegean.

Wild silks have an enduring globalized past which deserves attention in order to understand the history of silk/silkS as well as the importance of these materials in today's world.

Wild Silks Globalized materials in the longue durée

Between collections and living practices: comparative explorations

The social dimensions of several localised wild silks cultures are studied and compared through multi-sited ethnographies and historiographies.

• What kind of role have wild silks played in the diffusion of sericulture and weaving between Asia and Europe since the beginning of our era? • Are there specific features of today's practices that can help reconstruct how wild silks were transformed and circulated in the past? Detailed observations of the human handling of either the same species in different contexts or of different species in similar regions will help to uncover the socio-cultural and technical mechanisms that underline wild silks cultures, as well as to explore them as localized forms of cultural identities and values. Comparisons drawn between the studied regions and the ancient silks discovered by archaeologists and art historians will help us to refine the long term vision of wild silks cultures in global history. One example, from four figured silks, in wild and Bombyx mori silk with scenes from the life of Vishnu, probably Assam (India), late 16th to 18th c.

Collaborations with entomologists, physicians and chemists should help connect past and present and unveil some aspects of the wild silkS routes.

Early evidence of wild silks circulations in French collections

  @ehess.fr Shawl found in Antinoé, Egypt, in a tomb of the 5th-early 7th c.: wild silk and cotton with specific technical characteristics pointing to an Indian production. This piece may be the result of trade accross the Indian Ocean.© Musée des tissus, Lyon.

  When history, social anthropology, biochemistry and science of materials meet! The envelop of Saint Domnin's relics Found in the treasury of the Cathedral of Le-Puy-en-Velay (France), this non-woven wild silk fabric has been used to wrap relics (a few bones) of saint Domnin. It may have been introduced in the reliquary during the 9th, 13th, or 19th century. After many fanciful hypothesis, it is possibly a cocoon collectively built by processionary caterpillars as suggested by comparisons with such cocoons preserved in French collections (Confluences Museum, Lyon ; the quai Branly Museum, Paris), or investigated by L. Douny in West Africa. Indeed, moths, cocoons, yarns and textiles related to wild silks have been collected in various parts of the world during the second half of the 19 th and early 20 th century by European scientists and industrials looking for new species and/or new materials.

  School of Advance Studies in the Social Sciences), Centre for Historical Research (CRH), Paris, France

		Annabel Vallard 1 , Sophie Desrosiers 2
	1.	CNRS (National Centre for Scientific Research), Centre for Southeast Asian Studies (CASE), Paris, France
	2.	EHESS (