H Ayari

F Azais

S Bernard

M Comte

V Kerzerho

M Renovell

New implementions of predictive alternate analog/RF test with augmented model redundancy

Keywords: Test, analog/RF integrated circuits, alternate test, specification prediction, test confidence I

This paper discusses new implementations of the predictive alternate test strategy that exploit model redundancy in order to improve test confidence. The key idea is to build during the training phase, not only one regression model for each specification as in the classical implementation, but several regression models. This redundancy is then used during the testing phase to identify suspect predictions and remove the corresponding devices from the alternate test flow. In this paper, we explore various options for implementing model redundancy, based on the use of different indirect measurement combinations and/or different partitions of the training set. The proposed implementations are evaluated on a real case study for which we have production test data from 10,000 devices.

INTRODUCTION

The alternate test strategy is a promising solution to reduce the testing costs of analog/RF circuits. The basic idea of this strategy is to replace standard specification tests by a set of few alternate measurements obtained with low-cost test equipment, and to infer the results of specification testing using only these low-cost indirect measurements. This strategy therefore offers substantial test cost reduction by relaxing constraints on both the number and the complexity of required test configurations.

Alternate testing has been widely studied in the literature for many years [1][START_REF] Variyam | Prediction of analog performance parameters using fast transient testing[END_REF][START_REF] Ellouz | Combining Internal Probing with Artificial Neural Networks for Optimal RFIC Testing[END_REF][START_REF] Abdallah | Sensors for built-in alternate RF test[END_REF][START_REF] Barragan | Improving the Accuracy of RF Alternate Test Using Multi-VDD Conditions: Application to Envelope-Based Test of LNAs[END_REF][START_REF] Ayari | Smart selection of indirect parameters for DC-based alternate RF IC testing[END_REF][START_REF] Stratigopoulos | Error Moderation in Low-Cost Machine-Learning-Based Analog/RF Testing[END_REF][START_REF] Stratigopoulos | Adaptive alternate analog test[END_REF][START_REF] Ayari | On the use of redundancy to reduce prediction error in alternate analog/RF test[END_REF][START_REF] Ayari | Making predictive analog/RF alternate test strategy independent of training set size[END_REF]. Many aspects have been researched, such as the choice of the learning algorithm, the definition and optimization of appropriate test stimuli, the processing of complex signatures, the use of embedded sensors to gather pertinent information, the exploitation multi-Vdd test conditions and procedures for the selection of appropriate indirect measurements. Despite the number of good results reported in all these works that illustrate the efficiency of the alternate test strategy, its industrial deployment is still limited, mainly because of a confidence problem. To cope with this issue, an interesting approach is to use a two-tier test scheme in which devices for which the alternate test decision may be prone to error are identified and directed towards a different tier where further testing may apply [START_REF] Stratigopoulos | Error Moderation in Low-Cost Machine-Learning-Based Analog/RF Testing[END_REF]. Different solutions have been explored for the identification of suspect devices based either on kernel density estimation [START_REF] Stratigopoulos | Adaptive alternate analog test[END_REF] or on the use of redundancy [START_REF] Ayari | On the use of redundancy to reduce prediction error in alternate analog/RF test[END_REF][START_REF] Ayari | Making predictive analog/RF alternate test strategy independent of training set size[END_REF]. In this paper, we extend our previous work based on redundancy, and we explore various options for implementing model redundancy with the objective to strengthen the confidence in alternate test predictions.

II. ALTERNATE TEST PRINCIPLE

The underlying idea of alternate testing is that process variations that affect the conventional performance parameters of the device also affect non-conventional low-cost indirect parameters. If the correlation between the indirect parameter space and the performance parameter space can be established, then specifications may be verified using only the low-cost indirect signatures. Unfortunately the relation between these two sets of parameters is complex and cannot be simply identified with an analytic function. The solution commonly implemented uses machine-learning algorithms.

The alternate test principle is actually split into two sequential steps, namely training and production testing phases. The idea is to learn during the training phase the unknown dependency between the low-cost indirect parameters and the conventional test ones. For this, both the specification tests and the low-cost measurements are performed on a training set of device instances. The mapping derived from the training phase is then used during the production testing phase in order to perform device specification prediction or classification using only the low-cost indirect measurements. The classical implementation of predictive alternate testing is illustrated in Fig. 1.

III. PREVIOUS WORK AND LIMITATIONS

The alternate test strategy offers interesting perspectives for a low-cost test solution of analog/RF circuits. However this strategy is still not widely used in industry today, mainly because of a problem of confidence. Indeed although experiments reported in the literature show that good prediction accuracy can be achieved on various devices, in 978-3-9815370-2-4/DATE14/©2014 EDAA particular in terms of average prediction error, there are two main points that limit the credit one can give to this good accuracy. First, low average prediction error does not guarantee low maximal prediction error, which is of crucial importance regarding the classification step where the predicted values are compared to the specification limits promised in the data sheet. Second, evaluation is usually performed on a small set of validation devices, typically ranging from few hundreds to one thousand instances, while the technique aims at predicting values for a large set of fabricated devices, typically one or several millions.

In our previous work [START_REF] Ayari | On the use of redundancy to reduce prediction error in alternate analog/RF test[END_REF], experiments performed on a Power Amplifier (PA) fabricated by NXP Semiconductors for which we have production test data from 10,000 devices have revealed that the large majority of devices can indeed be accurately predicted using the alternate test strategy, but rather large prediction errors are observed for some circuits. Although the number of devices affected by such large prediction error is very small, i.e. much less than 1%, this is a serious obstacle for the deployment of the strategy in an industrial context. To cope with this issue, we have proposed a two-tier test scheme that includes an additional step during the testing phase in order to evaluate prediction confidence; if confidence is good, the device is evaluated using the low-cost alternate test tier otherwise it is directed to another tier for further testing. As illustrated in Fig. 2, the proposed scheme exploits model redundancy in order to order to distinguish reliable predictions from suspect predictions. More precisely, 3 regression models that involve different combinations of indirect measurements are built during the training phase for each specification. Then during the testing phase, prediction confidence is established by checking the consistency between the values predicted by the 3 different models, for each specification. For this, the difference between the predicted values is computed for each pair of models and checked against a threshold value  thi . If one (or more) of these differences is superior to ε thi , the prediction is considered suspect and the device is directed to the second tier where further testing may be applied. On the contrary, if all these differences are inferior to the threshold, the prediction is considered reliable and device specification is computed as the mean of the values predicted by the different models. Validation results obtained on the power amplifier case study have shown that, compared to a classical alternate test implementation, this scheme permits to achieve better performances in terms of both average and maximal prediction errors for devices evaluated by the alternate test tier while only a small fraction of the devices are directed to the second tier therefore incurring low test cost overhead.

The efficiency of the proposed scheme relies on the assumption that it is very unlikely that regression models built using different combinations of indirect measurements will erroneously predict the device performance with the same error. To verify this assumption, we have conducted a number of experiments on the power amplifier case study. Available production test data include 37 low-cost Indirect Measurements (IMs) based on standard DC tests and two RF performance measurements, namely the 1dB compression point (CP1) and 3rd order intercept point (IP3). These data are separated in two distinct sets of 5,000 devices, one used for training and the other for validation. Based on previous work showing that the RF performance parameters can be predicted with low average prediction error using models based only on few IMs [START_REF] Ayari | Smart selection of indirect parameters for DC-based alternate RF IC testing[END_REF], we have built regression models using all possible combinations of 3 IMs (7,770 models for each specification) and we have retained models with a relatively good accuracy (more than 5,000 models with an average prediction error below 2% for each specification). We have then evaluated the performances achieved by the proposed two-tier test scheme regarding CP1 specification when using 3 models randomly chosen among the retained models, repeating this experiment 100 times. As expected results show that, compared to the classical implementation with a single model, prediction errors are significantly reduced for all devices evaluated by the alternate test tier. However we denote one case where the procedure fails to identify a relatively large prediction error on one device of the validation set. For this case, the 3 regression models actually yield to an erroneous performance prediction with a similar error (difference between each pair of predicted values is less than 1dBm) for one particular device. The prediction is therefore not detected as a suspect one and the device is evaluated using the alternate test tier. So this is one limitation of the proposed approach.

IV. PROPOSED IMPLEMENTATIONS WITH AUGMENTED MODEL REDUNDANCY

Despite the use of 3 regression models based on different IM combinations, it may happen the 3 models erroneously predict a device performance with a similar error. In this case the procedure that checks prediction consistency is ineffective and the device is not directed towards the appropriate test tier. Our objective is to reinforce redundancy in order to avoid such situation. More precisely, the idea is to increase the number of redundant models used the procedure that checks prediction consistency in order to diminish the probability that all models give the same erroneous prediction for one device.

A first option to increase redundancy is to continue to exploit the different indirect measurements and to build, for each specification, not only 3 but a higher number of regression models based different IM combinations. However it is clear that selecting a higher number of different IM These results confirm the superiority of the new implementations with augmented model redundancy. Indeed although impact on the average prediction error is not significant, there is a substantial improvement regarding the maximal prediction error, with a reduction not only of the mean and maximum values observed over the different cases of generated redundant models, but also of the standard deviation. In particular, this standard deviation reduces from 0.42dBm with the initial implementation down to 0.28dBm for CP1 specification, and from 0.96dBm down to 0.5dBm for IP3 specification. This constitutes an important improvement of the robustness of the technique. Regarding comparison between the performances offered by the 3 versions of the new implementation, they are equivalent for CP1 specification, but version A leads to slightly better results for IP3 specification; this implementation may therefore be preferred. Regarding the cost-reduced implementation that exploit model redundancy based only on different training set partitions, this solution should not be retained as it presents degraded performances compared to other implementations.

Finally we have compared the different implementations regarding the percentage of circuits for which suspect predictions are identified. Results are summarized in Fig. 4. As expected, implementations with augmented model redundancy lead to a higher number of suspect predictions compared to implementations with model redundancy based only on either different IM combinations or different training set partitions, both for CP1 and IP3 specifications. However the percentage remains extremely low, less than 1.5%, which means that the new implementations permits to improve prediction results while maintaining a low test cost overhead. In this paper we have proposed new implementations of the predictive alternate test strategy that exploit model redundancy. These new implementations are based on redundant models that involve not only different combinations of indirect measurements as initially proposed, but also different partitions of the training set. Combining these two aspects permits the generation of a higher number of redundant models while maintaining the same cost, i.e. the same number of indirect measurements to be performed. The different implementations have been evaluated on a real case study for which we have production test data from 10,000 devices. Results have shown that implementations with reinforced model redundancy permit to reduce prediction errors of circuits evaluated by the alternate test tier, while maintaining a very small number of devices directed to a second tier for further testing.

Figure 1 .

 1 Figure 1. Predictive alternate test strategy

Figure 2 .

 2 Figure 2. Two-tier alternate test scheme using model redundancy

Figure 4 .

 4 Figure 4. Comparison of different implementations in tems of percentage of suspect predictions VI. CONCLUSION

TABLE I .

 I

			V. EXPERIM MENTAL RESUL LTS
			f experiments h have been per rformed on th he PA
			alidate the pro oposed strateg gy. First, we	have
			proposed imp plementations s considering g the
			ple discussed d in section		III. Results s are
			Table I that rep ports both ave erage and max ximal
			s observed for r the different t implementat tions.
			mentations wit th augmented		model redund dancy
			tioning of the		training set in n 3 disjoint sub bsets.
			aining set com mprises a rathe er large numb ber of
			are quite sensit tive to the rep partition of tra aining
			different sub bsets. Conseq quently, we c create
			splits of the tra aining devices		in 3 partition s and
			um, mean and d maximum va alues observed d over
			ns in this expe eriment). Fina ally for the sak ke of
			also report		results obtain ned when usi ing a
			plementation t that exploits m model redund dancy
			different train ning set partit tions (a single e IM
			considered an d only 3 redu undant model ls are
			different partit tions).
			sults of table I I, it can be o observed that t the 3
			new implem mentation of			augmented m model
			e equivalent p performances.		The efficienc cy of
			mentations is		clearly demon nstrated, since e they
			ce average a and maximal		prediction e errors
			e initial imple	mentation. Th he improveme ent is
			ificant regardi ing the maxim mal prediction	error
			m 4.08dBm w with the initi ial implement tation
			n 1dBm. Also		it can be obse erved that the	cost-
			entation that e xploits model l redundancy b based
			ent training		set partitions s offers degr raded
			mpared to othe er implementa ations.
			A AVERAGE AND MA AXIMAL PREDICTIO ON ERRORS FOR T THE
		PARTICUL LAR CP1 PREDICTI ION EXAMPLE OF		SECTION III
		Initial Implem l m.	New w Implementation ns Version A Version B V Version C	Co ost-redu uced Impl lem.
	min			1.17 %		1.17 %			1.17 %	1.65 5 %
	mean	1.28 % %	1.18 %		1.18 %			1.18 %	1.71 1 %
	max			1.19 %		1.19 %			1.20 %	1.76 6 %
	min			0.77 dBm		0.77 dBm	0	.78 dBm	2.03	dBm
	mean	4.08 dB Bm	0.81 dBm		0.81 dBm	0	.82 dBm	3.35	dBm
	max			0.96 dBm		0.96 dBm	0	.96 dBm	5.09	dBm
	Results on	the previous		CP1 predic	tion example e are
	tained conside ering 3 particu ular IM combin nations. To fu urther
	rroborate these e results, we h have conducted d a large camp paign
	experiments v varying the IM M combination ns used to buil ld the
	dundant model ls. More prec	isely for each h specification n, we
	rform 50 rando om selections		of 3 differen nt IM combina ations
	ong all the co ombinations c corresponding		to models w with a
	isfying accura acy. For each h 3 selected		IM combinat tions,
	dundant model s are then bui lt considering g 100 random	splits
	the training d devices in 3 p partitions. Imp plementations	with
	gmented mode el redundancy y are therefo ore evaluated	over
	00 different c cases of gener rated redundan nt models. Re esults
	summarized d in Tables		II and III f for CP1 and	IP3
	dictions respe ctively.


Jérôme Weiss

Pietro Bernardara

Michel Benoit

Modelling intersite dependence for regional frequency analysis of extreme marine events

Keywords: regional frequency analysis, pooling, intersite dependence, extremes, significant wave heights

The duration of observation at a site of interest is generally too low to reliably estimate marine extremes. Regional frequency analysis (RFA), by exploiting the similarity between sites, can help to reduce uncertainties inherent to local analyses. Extreme observations in a homogeneous region are especially assumed to follow a common regional distribution, up to a local index. The regional pooling method, by gathering observations from different sites into a regional sample, can be employed to estimate the regional distribution. However, such a procedure may be highly affected by intersite dependence in the regional sample. This paper derives a theoretical model of intersite dependence, dedicated to the regional pooling method in a "peaks over threshold" framework. This model expresses the tendency of sites to display a similar behavior during a storm generating extreme observations, by describing both the storm propagation in the region and the storm intensity. The proposed model allows the assessment of i) the regional effective duration of the regional sample and ii) different regional hazards, e.g., return periods of storms. An application to the estimation of extreme significant wave heights from the numerical sea-state database ANEMOC-2 is provided, where different patterns of regional dependence are highlighted.

Introduction

The design of off-shore structures, or coastal protections preventing shoreline areas from marine flooding, particularly requires an accurate estimation of the probability of occurrence of extreme marine events (e.g., extreme storm surges or wave heights). High return levels can be inferred through a local statistical analysis of extremes, from a time series observed at a given site. However, a potential issue is the local duration of observation, generally too low to accurately estimate return levels of interest. For example, wave records from buoys are usually shorter than 20-30 years.

Regional frequency analysis (RFA) can help to reduce these uncertainties, by exploiting the information shared by similar sites in a region. When based on the index-flood method [Dalrymple, 1960], RFA assumes that extreme observations in a homogeneous region follow a common regional probability distribution, up to a local index representing the local specificities of each site.

A possible approach to estimate the parameters of the regional distribution is the regional pooling method [START_REF] Bernardara | Application of the Regional Frequency Analysis to the estimation of extreme storm surges[END_REF]. The principle is to pool the data normalized by the local index in a single regional sample, the latter being used to fit the regional distribution. This method is also referred to as the station-year method [START_REF] Buishand | Extreme rainfall estimation by combining data from several sites[END_REF] and illustrates the principle of "trading space for time". However, it assumes intersite independence [START_REF] Cunnane | Methods and merits of regional flood frequency analysis[END_REF]Madsen and Rosbjerg, 1997;[START_REF] Stewart | The FORGEX method of rainfall growth estimation -I: Review of requirement[END_REF], which cannot be deemed realistic: indeed, for example, a storm is likely to generate dependent extremes at different sites. Thus, [START_REF] Dales | Regional flood and storm hazard assessment[END_REF] and [START_REF] Stewart | The FORGEX method of rainfall growth estimation -I: Review of requirement[END_REF] questioned the relevance of regional pooling when intersite dependence is ignored, and showed its approximate nature. Intersite dependence in regional pooling is actually closely related to the concept of regional effective duration [START_REF] Bernardara | Application of the Regional Frequency Analysis to the estimation of extreme storm surges[END_REF]].

The regional effective duration, denoted by D eff , can be defined as the effective duration of observation of the regional sample filtered of any intersite dependence. For example, if the times series recorded in different sites from a given region are considered independent, pooling data from 10 sites, each having 30 years of observation, is equivalent to sample 300 years of "effective duration". This is not the case in the presence of intersite dependence. At the same time, the highest independent normalized observation in the region is viewed as the largest in D eff years of record. It can be used to both reflect the relevance of RFA to a local analysis and to estimate empirical regional return periods. However, [START_REF] Kergadallan | Analyse statistique des niveaux d'eau extrêmes -Environnements maritime et estuarien[END_REF] pointed out that one limitation of RFA is the difficulty to evaluate D eff .

As an illustration, most of regional pooling studies are based on a simplifying hypothesis. For example, [START_REF] Hjalimarsom | New Look at Regional Flood Frequency Relations for Arid Lands[END_REF], [START_REF] Bernardara | Application of the Regional Frequency Analysis to the estimation of extreme storm surges[END_REF] and [START_REF] Bardet | Regional frequency analysis of extreme storm surges along the French coast[END_REF] assumed D eff as the sum of all the local durations, hence assuming intersite independency.

Dalrymple [1958] expressed that records cannot be expanded to yield an effective duration equal to the sum of local durations. In this work, it is conversely assumed that D eff can be formulated as the typical local duration, implicitly considering perfect intersite dependence.

The actual value is likely to lie between these two extreme cases. A realistic estimation of D eff requires a proper characterization of intersite dependence.

A consequence of intersite dependence is a loss of information [START_REF] Reed | Rainfall frequency analysis for flood design, in Coping with Floods[END_REF]. For example, when a storm impacts several sites, there is redundancy of information because observed extremes stem from the same meteorological event. Several studies assessed the effects of intersite dependence in the framework of RFA. For example, the effective size of samples is reduced [START_REF] Bayazit | Sampling variances of regional flood quantiles affected by intersitecorrelation[END_REF][START_REF] Buishand | Extreme rainfall estimation by combining data from several sites[END_REF][START_REF] Kjeldsen | Comparison of regional index flood estimation procedures based on the extreme value type I distribution[END_REF]Madsen and Rosbjerg, 1997;[START_REF] Rosbjerg | The role of regional information in estimation of extreme point rainfalls[END_REF]. [START_REF] Castellarin | Homogeneity testing : how homogeneous do heterogeneous cross-correlated regions seem[END_REF] also observed a decrease of the power of the homogeneity test proposed by [START_REF] Hosking | Some statistics useful in regional frequency analysis[END_REF]. [START_REF] Stedinger | Estimating a regional flood frequency distribution[END_REF], [START_REF] Hosking | The effect of intersite dependence on regional flood frequency analysis[END_REF] and [START_REF] Rosbjerg | The role of regional information in estimation of extreme point rainfalls[END_REF] showed that ignoring intersite dependence in RFA leads to an underestimation of the variance of return levels estimates. When at-site distributions are the main interest, [START_REF] Smith | Regional estimation from spatially dependent data[END_REF] suggests to initially ignore intersite dependence and then correcting a posteriori the regional variance.

A simple way to take into account intersite dependence is to remove it. Some authors proposed its filtering through a spatial declustering procedure, where events impacting several sites are counted only once. To estimate extreme surges with RFA, [START_REF] Bernardara | Application of the Regional Frequency Analysis to the estimation of extreme storm surges[END_REF] and [START_REF] Bardet | Regional frequency analysis of extreme storm surges along the French coast[END_REF] formed the regional sample with the highest observations among extremes occurring within 72 hours in the study area. However, the major disadvantage of such an approach is a significant loss of information on the spatial dynamics of extremes generated by a single storm. Moreover, this approach does not introduce any technique to estimate D eff .

. Intersite dependence can also be modeled. [START_REF] Cooley | A survey of spatial extremes : Measuring spatial dependence and modeling spatial effects[END_REF] and [START_REF] Bernard | Clustering of maxima: spatial dependencies among heavy rainfall in France[END_REF] deplored the lack of an explicit modeling of intersite dependence for RFA.

Nevertheless, [START_REF] Lang | Use of a gaussian copula for multivariate extreme value analysis : some case studies in hydrology[END_REF] and [START_REF] Renard | A bayesian hierarchical approach to regional frequency analysis[END_REF] represented the dependence of extreme rainfalls at different sites with elliptical copulas. Extremes at two different sites were also regionally modeled by [START_REF] Buishand | Bivariate extreme-value data and the station-year method[END_REF], through bivariate extreme value theory. An alternative approach, dedicated to annual maxima, was proposed by [START_REF] Dales | Regional flood and storm hazard assessment[END_REF]; it links distributions of the regional maximum and the typical regional data through an effective number of independent sites. Most of the papers cited above analyzed series of annual maxima. Yet, an alternative way is to consider exceedances over a high threshold with the "peaks over threshold" (POT) method [START_REF] Davison | Models for exceedances over high thresholds[END_REF]. Its superiority over methods based on annual maxima, for both local and regional estimation of extremes, was demonstrated by Madsen et al. [1997a], Madsen et al. [1997b] and [START_REF] Arns | Estimating extreme water level probabilities: A comparison of the direct methods and recommendations for best practice[END_REF]. Besides, the POT framework is more physically appealing to handle intersite dependence. For annual maxima, this one is characterized on a yearly basis, and may thus be difficult to interpret: for example, series of annual maxima observed at two distinct sites can be highly statistically correlated, without necessarily being caused by the same meteorological phenomena. Conversely, the POT framework allows reasoning at the scale of the physical event, provided that the concurrence of observations at different sites can be carefully defined [START_REF] Mikkelsen | Properties of extreme point rainfall III: Identification of spatial inter-site correlation structure[END_REF][START_REF] Stewart | The FORGEX method of rainfall growth estimation -I: Review of requirement[END_REF]. In particular, storms generating extreme observations offer an intuitive framework to deal with intersite dependence in a POT approach. [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF] characterized storms through the gathering of extremes neighbors in space and time, and described a procedure to detect them in the context of marine extremes. These storms allow to naturally define the concurrence of observations at the scale of the physical event.

Thus, very few studies addressed the issue of intersite dependence for RFA in a POT framework. [START_REF] Roth | A regional peaks-over-threshold model in a nonstationary climate[END_REF] used the model of [START_REF] Dales | Regional flood and storm hazard assessment[END_REF] by grouping POT data into seasonal blocks. It can be argued, that defining the concurrence of observations through a wide temporal block (the season) may result in a loss of information on both the spatial coverage and the intensity of the physical events generating extremes. [START_REF] Mikkelsen | Properties of extreme point rainfall III: Identification of spatial inter-site correlation structure[END_REF], [START_REF] Rosbjerg | The role of regional information in estimation of extreme point rainfalls[END_REF], [START_REF] Madsen | A regional Bayesian method for estimation of extreme streamflow droughts, Statistical and Bayesian methods in hydrological sciences[END_REF] and [START_REF] Madsen | Regional estimation of rainfall intensity-duration-frequency curves using generalized least squares regression of partial duration series statistics[END_REF] proposed regional regression models, which are not based on the index-flood procedure used in this paper. Similar to geostatistics, their models explicitly account for intersite correlation, where the concurrence of observations is defined through the overlap of POT data in a short time window. Madsen and Rosbjerg [1997] corrected the variance of the regional distribution parameters with an effective number of independent sites, based on a regional average correlation coefficient. However, in the latter references, although the concurrence of observations is defined in a physically appealing way, only the pairwise dependence is modeled. Moving towards a more global model of intersite dependence indicating, for example, the tendency of sites in a region to behave similarly during a storm, would help to characterize different regional hazards.

The estimation of extreme events by RFA allows to tackle the open question of the difference between regional and local return period. In particular, note that to estimate the return period of a storm affecting a given area, synoptic variables are usually defined first.

Della-Marta and [START_REF] Della-Marta | Statistical uncertainty of changes in winter storms over the North Atlantic and Europe in an ensemble of transient climate simulations[END_REF] characterized a storm by the minimum central pressure and the maximum vorticity reached during its track; [START_REF] Pinto | Loss potentials associated with European windstorms under future climate conditions[END_REF] used the wind speed maximum; a more general spatial index, reflecting both the magnitude and the spatial extent, was defined by Della-Marta et al. [2009], who then estimated the return period from these synoptic variables. By construction, such an estimate corresponds to a "regional" return period, namely the return period of a storm which can occur anywhere in the study area.

However, for practical applications (e.g., protection design), a local return period must be estimated. For example, it is clear that a storm whose regional return period is 50 years will not generate everywhere in the area wave heights (or storm surges) corresponding to a 50year return period. In particular, the link between the regional return period of a storm and the return period of a given observed variable generated by the storm at a particular location remains unknown. Note that Della-Marta et al. [2009] showed that regional return periods share up to about half of the variability of the local return periods. In this study, we will show how a proper treatment of intersite dependence can help to describe the relation between the regional and the local return period of a storm.

The objective of this paper is to develop a global model of intersite dependence for RFA, specifically dedicated to the regional pooling method and POT data, by reasoning at the storm scale. Distributions of the regional storm maximum and the typical regional storm data are linked through a function of regional dependence, describing both the propagation of storms and their regional intensity. The proposed model allows the derivation of different regional hazards and the regional effective duration.

The model of regional dependence is developed in section 2, including its implications on the regional pooling method (section 2.4). An application to the estimation of extreme significant wave heights from the numerical database ANEMOC-2 is shown in section 3.

Methodology

Extraction of storms

To characterize the intersite dependence, it is first necessary to define the simultaneity of observations in space. If data are sampled every hour, the reference for simultaneity can be, for example, the hourly scale. However, as extreme oceano-meteorological conditions can last from several hours to several days, the temporal dimension should be added to describe the spatial dependence. In this paper, the scale of the physical events generating marine extremes (storms) is taken as the reference to define the simultaneity of observations in space.

A storm is thus directly characterized through the variable of interest (e.g., wave height or storm surge), being defined as a physical event generating marine extremes in at least one site in the study area. In the literature, the tracking of storms often relies on a nearestneighbor search in space and time [e.g., [START_REF] Leckebusch | Development and application of an objective storm severity measure for the Northeast Atlantic region[END_REF]Renggli et al., 2010]. A spatiotemporal declustering procedure is thus employed to detect storms and to reflect their propagation in space and time. In particular, extremes neighbors in space and time are supposed to stem from the same storm. The storm extraction algorithm in the context of marine extremes is described in [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF], trying to reproduce at best the physical dynamics of the storms, while taking into account the spatio-temporal resolution of observations. Moreover, a "double-threshold" approach is employed to separate physical considerations from statistical ones [START_REF] Bernardara | A two-step framework for over-threshold modelling of environmental extremes[END_REF].

At a given site, the impact of a storm is characterized by observations exceeding the "physical threshold" q p , defined as the p-quantile of the initial time series, with p close to 1. In order to get independent data at site scale, only the peak value i s W is retained to summarize the storm s at site i (which implies that all other extremes occurring during that storm are discarded).

Only the most intense storm events are now considered for statistical aspects. New thresholds, denoted u and higher than the quantiles q p , are selected corresponding to the occurrence of λ storms per year on average at each site. In particular, if d i years of data are available at site i, the n i = λd i highest i s W are retained to form the n i -sample i s X . The "statistical threshold" u i , exceeded on average λ times per year, is then defined as the smallest observation from i s X (minus an infinitesimal quantity). Storms are then statistically redefined: if site i was impacted by storm s, it is from now on impacted by s if and only if u i is exceeded.

Regional frequency analysis

Extreme events are estimated in this paper from exceedances over a high threshold.

According to [START_REF] Pickands | Statistical Inference Using Extreme Order Statistics[END_REF], the Generalized Pareto Distribution (GPD) represents the natural distribution for such exceedances. For ease of notation, the index s denoting the storm is omitted in this section. For site i, let u i be the storm threshold which is exceeded on average λ times per year. The n i -sample X i , denoting the exceedances of u i , is assumed to be drawn from a GPD: X i ~ GPD(u i , α i , k i ), where α i > 0 and k i are, respectively, a scale and a shape parameter. In particular, the p-quantile of X i is:

     0 ), - 1 log( - 0 ≠ ), ) - 1 ( - 1 ( - - i i i i k i i i i p k p u k p k α u x i  (1)
The right tail of the GPD is bounded when k i < 0, and unbounded when k i ≥ 0. The T-year return level, i.e., the value exceeded on average once every T years, is given by i T λ

x 1 -1 [START_REF] Rosbjerg | Estimation in partial duration series with independent and dependent peak values[END_REF].

A homogeneity hypothesis is required for RFA based on the index-flood method.

Observations from sites coming from a homogeneous region are supposed to follow the same regional probability distribution, up to a local index representing the local specificities of a site. In this paper, homogeneous regions are formed following [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF], where typical storm footprints are identified with a clustering algorithm based on a criterion of storm propagation. In particular, sites from a given region are likely to be impacted by the same storms, and any storm impacting a region is likely to remain enclosed in this region.

For a homogenous region of N sites, let μ i be the local index of the site i = 1,…,N. The [START_REF] Roth | A regional peaks-over-threshold model in a nonstationary climate[END_REF] showed that dealing with exceedances over a high threshold necessarily implies that the local index has to be a multiple of this threshold. Here, as in [START_REF] Roth | A regional peaks-over-threshold model in a nonstationary climate[END_REF] and [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF], μ i is therefore chosen as the threshold u i . This implies that Y ~ GPD(1, γ, k), where: i) the regional scale parameter satisfies γ = α i / u i and ii) the shape parameter k i = k is constant over the region. From these relationships, X i ~ GPD(u i , γu i , k). For site i, the T-year return level is obtained by multiplying the regional T-year return level by the local index:

normalized variable Y = X i / μ i is supposed to be independent of i, with cumulative distribution function (c.d.f.) F r .
T λ i i T λ y u x 1 - 1 1 - 1 = .
The two regional parameters (γ, k) can be estimated with the regional pooling method.

However, as sites in a region are likely to be impacted by the same storms, a strong intersite dependence is expected. If ignored, this may affect the estimation process. Thus, this dependence is firstly modeled as outlined in section 2.3, before the regional pooling method is described in section 2.4.

Modeling of regional dependence

Notations

Let λ r be the mean annual number of storms in the region and i s Z the Bernoulli variable which is 1 if storm s impacts site i and 0 otherwise. When storm s impacts site i, the observed normalized extreme with c.d.f. F r is denoted by , where

i i s i s u X Y / = . Note that i s Y ≥ 1.
i s i s i s Z Y η =
. The storm regional maximum is then defined as

i s N i s η M ,.., 1 = max =
. As at least one site is impacted by the storm s, M s ≥ 1.

Distribution of the storm regional maximum

First, note that due to the statistical redefinition of storms at the end of section 2.1, i s Z takes the value 1 with probability λ / λ r , independently of i. Moreover, by the regional homogeneity hypothesis from section 2.2, the distribution of i s η does not depend on i:

)) ( - 1 ( = ) 1 = | > ( ) 1 = ( = ) > ( , 1 ≥ ∀ x F λ λ Z x η P Z P x η P x r r i s i s i s i s (2)
For x ≥ 1, the distribution of M s can be obtained through the following decomposition:

) > ( + ) ≤ max , > ( = ) > max ( = ) > ( ∑ 1 - 1 = ,.., 1 + = ,.., 1 = x η P x η x η P x η P x M P N s N i j s N i j i s i s N i s (3) Now, as the distribution of i s η is independent of i: ] ) > | ≤ max ( + 1 )[ > ( = ) > ( ∑ 1 - 1 = ,.., 1 + = 1 N i i s j s N i j s s x η x η P x η P x M P (4)
From (2), this leads to:

) ( )) ( - 1 ( = ) ( ) > ( = ) > ( 1 x φ λ λ x F x φ x η P x M P r r s s (5) where 1 ≥ , ) > | ≤ max ( + 1 = ) ( ∑ 1 - 1 = ,.., 1 + = x x η x η P x φ N i i s j s N i j (6)
The distribution of M s can be thus written in terms of the regional distribution F r and φ.

Characterization of the regional dependence

The function φ reflects the regional dependence. Situations of independence and perfect dependence, illustrating extreme cases of dependence, can be reinterpreted through equation ( 6) with x = 1. In particular, the region is regional-independent (r -⫫) if and only if φ ≡ N; in that case, a storm impacts only one site in the region, whatever its intensity.

Conversely, the region is perfectly regional-dependent (p-rd) if and only if φ ≡ 1; a storm impacts every site in the region and, whatever its intensity, the generated (normalized) extremes vary the same way. Between these two extremal situations, φ takes values between 1 and N.

By construction, φ relates both the storm propagation in the region and the storm intensity. It expresses the tendency of sites to display a similar behavior during a storm. The regional dependence is stronger when φ is small, hence indicating that most of the sites are impacted by a storm, and are likely to react the same way in terms of normalized extremes.

φ is influenced by the number N of sites in the region. In order to compare φ between different regions, the effect of N can be removed through the following adimensional function:

1 ≥ , 1 - ) ( - = ) ( Φ x N x φ N x (7)
where Φ, lying between 0 and 1, is near to 1 when regional dependence is strong.

Assessment of regional hazards

A regional hazard is an event occurring at the regional scale, whose probabilistic description is related to collective risk assessment. The following examples of regional hazards are expressed in terms of the function of regional dependence φ.

A first example is the mean number β s (x) of impacted sites with normalized intensity larger than x ≥ 1 when the storm regional maximum is larger than x:

] 1 [ = ) ( ∑ 1 = > | > N i x M x η s s i s E x β (8)
From equation ( 5):

) ( = ) > ( ) > ( = ) > | > ( = ) ( 1 1 x φ N x M P x η P N x M x η NP x β s s s s s (9)
In particular, the mean number of impacted sites during any storm is given by β s (1) = N / φ(1).

Note that this is coherent with the definitions of regional-independence and perfect regionaldependence.

Another example is the evaluation of the regional return period of a particular storm, and how it is related to its local return period. Let s be a given storm, and denote by x ≥ 1 its corresponding normalized intensity. The regional return period of s, T r , is defined as the average time between storms impacting at least one site in the region with a normalized intensity greater than x, i.e.:

) > ( 1 = x M P λ T s r r (10)
The local return period of s, T, is defined as the average time between storms impacting a given site in the region with a normalized intensity greater than x:

)) ( - 1 ( 1 = x F λ T r (11)
From ( 5), T r and T are related through:

) ( = x φ T T r (12)
2.4 Regional pooling method 2.4.1 Construction of the regional sample

The regional pooling method is used to estimate the regional distribution F r . However, due to the presence of intersite dependence, events impacting several sites must be counted only once. Storms presented in section 2.1 are a convenient way to filter intersite dependence, as each storm describes the regional footprint of a particular event generating extremes.

In particular, the distribution of the storm regional maximum M s is now assumed to be the same as the regional distribution F r . This assumption was implicitly made in [START_REF] Bernardara | Application of the Regional Frequency Analysis to the estimation of extreme storm surges[END_REF] and [START_REF] Bardet | Regional frequency analysis of extreme storm surges along the French coast[END_REF], where the regional distribution was estimated from the highest normalized surges occurred within 72 hours in the region. In other words, the distribution of the maximum of a regional cluster is identical to the distribution of a generic element of this cluster. The same assumption is often made in a POT time series framework, as explained by Anderson in the discussion of the paper by Davison and [START_REF] Smith | Regional estimation from spatially dependent data[END_REF]: "this apparent paradox is a consequence of length-biased sampling: a randomly chosen exceedance has a disproportionate chance of coming from a large cluster, and in large clusters there tend to be large excesses." However, in practice, the validity of this assumption must be verified. For example, the two-sample Anderson-Darling test [START_REF] Scholz | K-sample Anderson-Darling Tests[END_REF] can be performed at each site i to evaluate the null hypothesis that i s Y and M s have the same distribution.

If n r independent storms are observed in the region, the regional sample is thus formed by the n r -sample of storm regional maxima M s , and corresponds to D eff years of regional effective duration.

The assumption that the storm regional maximum M s is the same as the regional distribution F r depends on the data at hand. When this hypothesis is not verified, the following alternative strategies nevertheless allow to perform a RFA: i) Remove sites of which Anderson-Darling p-values are too low (for example, lower than 0.01) to accept this hypothesis. The application of the model of regional dependence and the estimation of F r can then be performed on the remaining sites.

ii) Form the regional sample with random (normalized) observations from each storm, instead of using the storm regional maxima M s . F r can still be estimated by pooling, directly from this new regional sample. However, the simplified model of dependence (section 2.4.3) is not valid anymore, as φ is not a constant function. It would be possible to update equation ( 14) by letting the regional effective duration depend on regional quantiles.

iii) Use another method to perform the RFA, e.g., the regional L-moments method of [START_REF] Hosking | Regional Frequency Analysis. An approach based on L-moments[END_REF]. The model of regional dependence developed in this paper, dedicated to the pooling method, does not apply anymore in this case.

Estimation of the regional distribution F r .

The two regional parameters (γ, k), see section 2.2, are estimated from the regional sample. Penalized maximum likelihood estimation (PMLE) [START_REF] Coles | Likelihood-Based Inference for Extreme Value Models[END_REF] is used in this study. The principle is to combine the efficiency of maximum likelihood estimators for large sample sizes and the reliability of the probability weighted moment estimators for small sample sizes. In particular, high estimates of the shape parameter k are penalized. PMLE is implemented in the function fitgpd of the POT package [START_REF] Ribatet | POT: Modelling Peaks Over a Threshold[END_REF], in the statistical computing environment R (R Development Core Team, 2013). Uncertainties on estimates of (γ, k) are here assessed with a bootstrap procedure: 10,000 replications of the (γ, k) values are obtained with PMLE from resamples of the regional sample.

Simplification of the model of regional dependence

The regional pooling method presented in this paper assumes that the distribution of the storm regional maximum M s is the same as the regional distribution F r . The model of regional dependence in section 2.3 can thus be simplified. Indeed, from (5), this assumption implies that φ becomes a constant function:

λ λ x φ x F x M P x r r s = ) ( ↔ ) ( - 1 = ) > ( , 1 ≥ ∀ ( 13
)
As φ is constant, the way sites react during a storm does not depend on the intensity of the storm. Similarly, [START_REF] Dales | Regional flood and storm hazard assessment[END_REF] applied their model to rainfall annual maxima and observed that the effective number of sites, summarizing the spatial dependence, did not seem to depend on a particular regional intensity.

The regional effective duration D eff

The pooling procedure yields D eff years of regional effective duration. D eff is closely related to the degree of regional dependence; in particular, D eff is expected to be low when regional dependence is strong.

First, the two simplistic situations of regional dependence (section 2.3.3) are considered. Let d = ∑d i / N be the mean local duration, where d i is the local duration of observation at site i and N is the number of sites in the region. If the region is r -⫫, a storm impacts only one site in the region. In that case, each observation from any site brings new information, and D eff can be written as the sum of all the local durations:

D eff = N d .
Conversely, if the region is p-rd, a storm impacts every site in the region. Here, the typical local duration of one site constitutes D eff , as the information from other sites is purely redundant. This can be reflected by taking, for example, D eff as the mean local duration: D eff = d . It is now assumed that, between these two extremal cases, D eff can be more realistically expressed by:

D eff = φ d (14)
where φ, lying between 1 and N, is the degree of regional dependence. Note that the situations of p-rd and r -⫫ are respectively obtained for φ = 1 and φ = N. From equation ( 13), stating that φ = λ r / λ, its theoretical value is

D eff = λ r d / λ.
The mean annual number of storms in the region λ r can be naturally estimated by n r / d , where n r is the number of observed storms. An estimate of D eff is then:

λ n D r eff = ˆ ( 15
)
Let n r,t be the number of observed storms during year t = t 1 ,…,t τ in the region, where t 1 and t τ indicate the first and the last year of observation in the region, respectively. The overall number of observed storms n r is obtained by summing the n r,t for t = t 1 ,…,t τ . By assuming that the n r,t are independent and identically distributed with common mean λ r and standard deviation σ r , the central limit theorem followed by the Slutsky's lemma allow to derive new confidence intervals for

D eff : ] + , - [ 2 / - 1 2 / - 1 λ τ σ z D λ τ σ z D r α eff r α eff (16) where 2 / - 1 α z
is the quantile of order 1-α/2 of the standard normal distribution, r σ ˆ is the empirical standard deviation of the n r,t, and τ is the number of years of observation in the region.

Note that ( 15) can be used even if periods of observations are different, and in the presence of missing data. This formula also guarantees that

i N i eff d D ,.., 1 = max ≥ ˆ, coherently with
what might be expected from the regional effective duration. Besides, it reflects the importance to extract storms such that their mean annual occurrence λ at the local scale is common to all sites.

As F r is estimated from D eff years of pooled data, the underlying principle is that any site in the region can be indifferently impacted by a given storm. Parenthetically, with no preferential storm track in the region, the regional pooling method is coherent with the identification of storms footprints to form homogeneous regions. In particular, the regional sample illustrates that, for a generic site, λ storms per year, on average, were observed during D eff years. D eff thus helps to reflect the relevance of RFA to a local analysis. Indeed, pooling enables to estimate extreme events at site i from D eff years of data, compared to d i years for a local analysis.

Evaluation of storm return periods

The regional pooling method allows to distinguish between local and regional return periods of normalized storm events (see section 2.3.4 for the corresponding definitions), both at the empirical and theoretical levels. Let s be a given storm from the regional sample, and denote by x its corresponding normalized intensity.

Using the Weibull plotting position, its empirical local return period loc s T , ~ is:

) rank( - 1 + 1 + = ~, s n D T r eff loc s (17)
where rank(s) denotes the rank of s in the regional sample. For example, if s is the most intense storm observed in the regional sample, then loc s T , ~ is about D eff years. Besides, the theoretical local return period loc s T , of s is given by equation ( 11). We recall that loc s T , corresponds to the theoretical return period of storm s at site scale (i.e., at any site of the region). Using ( 12) and ( 13), the theoretical regional return period reg s T , is given by:

loc s r reg s T λ λ T , , = (18)
The empirical regional return period [START_REF] Laugel | Sea state climatology in the North-East Atlantic Ocean: analysis of the present climate and future evolutions under climate change scenarios by means of dynamical and statistical downscaling methods[END_REF]. The simulations of wave conditions have been carried out with the third-generation spectral wave model TOMAWAC [START_REF] Benoit | Development of a third generation shallow-water wave model with unstructured spatial meshing[END_REF] forced by wind fields from the CFSR reanalysis database [START_REF] Saha | The NCEP Climate Forecast System Reanalysis[END_REF].

The spatial resolution of the so-called "oceanic mesh" of ANEMOC-2 ranges from about 120 km over the Northern part of the Atlantic Ocean down to about 20 km along the European coast and 10 km along the French coast. Note this grid is supplemented by a "coastal mesh" whose resolution is finer on the continental shelf, in the Channel and along the French coast. For the present study, however, only data from the oceanic mesh is used, and only a subset of 1847 nodes amongst the 13426 nodes of the full oceanic mesh is selected, at locations plotted in Figure 1.

Among the wave parameters available with an hourly resolution in ANEMOC-2, we consider here the significant wave height, denoted H s , which is usually the preferred parameter to summarize sea state intensity. TOMAWAC computes this wave height from the zero-order moment of the wave spectrum. Hourly series of significant wave heights H s over the period 1979-2009 are thus extracted for the 1847 selected sites. The objective here is to apply the proposed methodology i) to characterize the regional dependence over this area and ii) to estimate extreme H s by the regional pooling method.

Preparation of data for RFA

More details for this section may be found in [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF], where the same dataset was used.

The physical extraction of storms generating extreme H s , described in the beginning of section 2.1 with p = 0.995, leads to 5939 storms. [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF] performed a sensitivity analysis and found that storms are properly detected when p = 0.995. A quick analysis reveals that, on average: i) there are 192 storms per year in the study area, ii) a storm impacts 38 sites and iii) a storm lasts 12.5 hours at site scale. These storms serve to form physically homogeneous regions, by detecting the most typical storms footprints in the study area. The footprints of the storms of 15-18 February 1986, 11-13 December 1990and 23-24 January 2009 (Klaus) are shown in Figure 2.

Storms are then statistically redefined, following the methodology presented in section 2.1. In particular, λ = 1 storm per year are now observed, on average, at each site; 1340 storms are thus retained among the 5939 initial ones. Site i is therefore characterized by the sample of H s over the threshold u i exceeded on average once per year; the sample size is 31, as 31 years of data are available. These thresholds, represented in Figure 3, are also the local indices used for RFA (section 2.2). These storms serve to i) check the statistical homogeneity of the physically homogeneous regions, ii) deal with regional dependence and iii) estimate extreme events with the regional pooling method.

RFA can thus be performed on each of the six homogeneous regions delineated in [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF], see Figure 4.

Regional pooling method

For each of the six regions, the regional sample is constructed by pooling the observed normalized storm regional maxima, following section 2.4.1. To check whether the storm regional maxima are sampled from the regional distribution F r , the two-sample Anderson-Darling test is performed. The p-values for the null hypothesis that i s Y and M s have the same distribution, for each site i from a given region, are higher than 0.01 for 95% of all sites.

Therefore, it may be reasonably assumed that i) the model of regional dependence can be simplified and ii) F r can be estimated from the regional sample.

Measures of regional dependence

For each region, Table 1 provides some measures of regional dependence defined in sections 2.3.3, 2.3.4 and 2.4.4. Note that there are no missing values in ANEMOC-2 data, and periods of observations are the same for all sites (with a common local duration of d = 31 years).

Storms are, respectively, most and least most frequent in regions 2 and 6, with 25.2 and 2.7 storms per year on average. This is explained here by their size: regions 2 and 6 are, respectively, the largest and the smallest in terms of the number of sites. To compare the degree of regional dependence between regions, this size effect can be removed through the adimensional function Φ defined in equation ( 7). The regional dependence is thus the strongest in region 5, meaning that sites in this region tend to behave highly similarly during a storm: a large proportion of them are impacted, and the normalized extremes are likely to vary the same way. Conversely, the regional dependence is the weakest in region 2. This can be precised by considering the mean number β s (1) of impacted sites during a storm, see equation ( 9). Indeed, on average, a storm in region 2 only impacts 18.9 sites (4% of the region), whereas a storm in region 5 impacts 56.6 sites (24% of the region).

The regional effective duration D eff and its corresponding 95% confidence interval are estimated following equations ( 15) and (16). For example, pooling data from the 234 sites of region 5 enables to get a regional sample with D eff = 128 years of independent observations. Note that taking into account the regional dependence considerably reduces what would be obtained under the assumption of intersite independence (in that case, D eff = Nd = 7254 years).

Figure 5 shows the evolution of the regional return period T r against the local return period T for each region, see equation ( 12). Note that curves for regions 3 and 4 are very close to each other, giving the impression of being superimposed. The simplified model of regional dependence implies that T r and T are linearly related. For fixed T, T r is, respectively, the lowest and the highest in regions 2 and 6. For example, Table 1 gives 100 r , i.e., T r corresponding to T = 100 years. 100 r = 3.964 years in region 2: about every four years on average, a storm in this region causes at least one local 100-year event. Besides, although region 1 is much larger that region 3, note that their 100 r estimates are similar (about 10 years). If intersite dependence was assumed, then this quantity would have been, in proportion, much higher in region 3 than in region 1. However, the compensation is due to a stronger regional dependence in region 1. Thus, modeling the regional dependence allows a more realistic assessment of regional hazards.

Estimation of extreme H s

For each of the six homogeneous regions, the regional GPD parameters (γ, k) are estimated following the procedure outlined in section 2.4.2. These quantities are given in Table 2, as well as the 100-year regional return level y 0.99 . The shape parameter k is positive (corresponding to an unbounded GPD) in regions 1, 4 and 6, suggesting a higher intensity of extreme H s . The return level plots for each of the six regional distributions, together with the 95% confidence intervals obtained by bootstrap, are given in Figure 6. Note that the plotting position depending on the regional effective duration (equation ( 17)) is used to represent observations from the regional sample, hence allowing the estimation of empirical return periods (see section 3.3.3 for an application to the most intense storms observed).

At-site return levels are obtained by multiplying regional return levels by the local indices. Figure 7 shows the map of the estimated at-site 100-year H s . Estimates for coastal areas are not shown because, as mentioned in section 3.1, the present analysis uses data from the oceanic model of ANEMOC-2, whose resolution is not sufficient for these coastal areas and which includes only parts of the shallow-water effects. In a follow-up of this study, data from the coastal model may improve the simulated sea states in coastal areas. One can note on Figure 7 that 100-year H s estimates display a coherent spatial pattern, with lower values near the West European coasts. The highest return levels are obtained for sites located in the northcentral part of the study area (up to 29.65 m). Note that these estimates are comparable to those from [START_REF] Caires | 100-year return value estimates for ocean wind speed and significant wave height from the ERA-40 data[END_REF] and [START_REF] Weiss | Formation of homogeneous regions for regional frequency analysis of extreme significant wave heights[END_REF].

Compared to a local statistical analysis, the regional pooling method can help to reduce uncertainties in the estimation of extreme events, at a given site. Indeed, extrapolations from a local analysis would be based here on d = 31 years of observations; the regional pooling makes available D eff > d years of data for any site.

Return periods of the most intense storms observed

From the numeric database ANEMOC-2, storms with the highest normalized intensity were observed on February 1986, February 1979, December 1990, February 1988, December 1989 and January 2009, respectively in region 1, 2, 3, 4, 5 and 6. Figure 2 displays these storms which occurred in regions 1, 3 and 6.

As an application of section 2.4.5, return periods of these storms are provided in Table 3, both at the local and regional scales (empirical and theoretical). For example, in region 3, the empirical local return period loc s T , ~ of the storm of 11-13 December 1990 is estimated at 280 years. Its theoretical counterpart is quite close ( loc s T , = 367 years), as indicated by the return level plot for this region (Figure 6). As such a storm was observed only once in 31 years of observations in this region, its empirical regional return period reg s T , ~ is logically estimated at 31 years. From equation ( 18), the model of regional dependence predicts a theoretical regional return period reg s T , of 41 years.

Conclusions

By exploiting the information shared by statistically similar sites, regional frequency analysis (RFA) can reduce uncertainties in the estimations of high return levels, when at-site durations of observations are short. It is assumed that, in a homogeneous region, extreme observations follow a common regional probability distribution, up to a local index representing the local specificities of a site.

The method of regional pooling is employed in this paper, where normalized observations from different sites are gathered into a regional sample to estimate the regional distribution. In particular, this pooling procedure allows to define D eff years of regional effective duration. D eff is actually closely related to the degree of intersite dependence: for example, D eff is expected to be low when the dependence is strong. Intersite independence is a usual assumption in the literature and practice, although unrealistic: a storm is likely to generate dependent extremes at different sites. We have therefore proposed a theoretical frame to model intersite dependence for the regional pooling method.

Storms are here identified by detecting physical events generating extremes in at least one site in the study area; their spatio-temporal propagation is taken into account through the gathering of extremes neighbors in space and time. Storms allow to naturally define the concurrence of observations at the scale of the physical event, hence enabling to perform a RFA within a "peaks over threshold" framework. These storms represent a convenient way to describe regional dependence. In particular, they are the basis to i) construct the regional sample, by filtering the redundancy of information and ii) model the regional dependence.

The distribution of the storm regional maximum is linked to the regional distribution through a function of regional dependence. This function, describing both the storm propagation in the region and the storm intensity, expresses the tendency of sites to display a similar behavior during a storm. The proposed model allows i) a proper evaluation of D eff and ii) the assessment of different regional hazards: for example, the mean number of impacted sites during a storm, or return periods of storms both at the local and regional scales can be theoretically derived.

An application to significant wave heights from the numerical sea-state database ANEMOC-2 has been provided to demonstrate the capabilities of the model. Six homogeneous regions, corresponding to the most typical storms footprints were delineated in the North-East part of the Atlantic Ocean. Different patterns of regional dependence have been characterized in this area, before applying the regional pooling method to estimate extreme significant wave heights.

Although the proposed example considers significant wave heights, the method can easily be applied to other marine variables. Indeed, it is variable-oriented, in the sense that storms are specifically defined through to the variable of interest only. Moreover, D eff can also be estimated when periods of observations are not the same for all sites, and/or in the presence of missing values. Future works could, for example, apply the proposed model to other marine hazards (e.g., storm surges) to compare how regional dependence manifests compared to significant wave heights.

Acknowledgments

The permission to publish the results of this ongoing research study was granted by the Electricité de France (EDF) company. The results in this paper should, of course, be considered as R&D exercises without any significance or embedded commitments upon the real behavior of the EDF power facilities or its regulatory control and licensing. The authors would like to thank Amélie Laugel who kindly provided the ANEMOC-2 data used in this study, and the three anonymous reviewers who improved this paper by their constructive comments and suggestions. The wave data set used for the analyses presented in this article has been extracted from the ANEMOC-2 database. This dataset can be obtained by request addressed to the corresponding author. The use of this data is restricted to research purpose, all industrial or commercial applications being excluded.

Table 1. Measures of regional dependence for each region (with the number of sites N indicated between parentheses): λ r is the mean annual number of storms in the region, Φ is the adimensional function of regional dependence, β s (1) is the mean number of impacted sites during a storm, 100 r is the regional return period (in years) of the storm causing at least one local 100-year event (equation ( 12) with T = 100) and D eff is the regional effective duration (in years, along with the 95% confidence interval).

Table 2. Parameters of the regional distribution: γ (GPD scale parameter), k (GPD shape parameter), y 0.99 (100-year regional return level). T , are respectively the empirical local return period, the theoretical local return period, the empirical regional return period and the theoretical regional return period. Regional return period T r against the local return period T for each region, as defined in equation ( 12). Curves for regions 3 and 4 are superimposed.

Figure captions

Figure 6. Return level plots of the regional distributions (crosses represent observations from each regional sample), together with the 95% confidence intervals obtained by bootstrap. Regional return period T r against the local return period T for each region, as defined in equation ( 12). Curves for regions 3 and 4 are superimposed.

Figure 6. Return level plots of the regional distributions (crosses represent observations from each regional sample), together with the 95% confidence intervals obtained by bootstrap.

Figure 7.

Map of estimated 100-year H s (m).

Figure 1 .

 1 Figure 1.Location of the 1847 sites extracted from the oceanic mesh of the ANEMOC-2

Figure 2 .

 2 Figure 2. Footprints of the storms of a) 15-18 February 1986, b) 11-13 December 1990

Figure 3 .

 3 Figure 3.Map of threshold values of H s exceeded on average once per year (m).

Figure 4 .

 4 Figure 4. Division into six homogeneous regions.

  Figure 5.Regional return period T r against the local return period T for each region, as

Figure 7 .

 7 Figure 7.Map of estimated 100-year H s (m).

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2. Footprints of the storms of a) 15-18 February 1986, b) 11-13 December 1990 and c) 23-24

Figure 3 .

 3 Figure 3.

Figure 4 .

 4 Figure 4. Division into six homogeneous regions.

  Figure 5.

  The storm s can be summarized in the region by the multivariate random variable

	η	s	( = 1 s η	,...,	η	N s	)

Table 3 .

 3 Return periods (in years) of the storms with the highest normalized intensity

	observed in each region: loc s T , ~,	loc T , , reg s s T , ~	and reg s


Mathieu Mangeot
email: mathieu.mangeot@imag.fr

MotàMot project: conversion of a French-Khmer published dictionary for building a multilingual lexical system

Keywords: French-Khmer dictionary, MotÀMot, Jibiki

Economic issues related to the information processing techniques are very important. The development of such technologies is a major asset for developing countries like Cambodia and Laos, and emerging ones like Vietnam, Malaysia and Thailand. The MotAMot project aims to computerize an under-resourced language: Khmer, spoken mainly in Cambodia. The main goal of the project is the development of a multilingual lexical system targeted for Khmer. The macrostructure is a pivot one with each word sense of each language linked to a pivot axi. The microstructure comes from a simplification of the explanatory and combinatory dictionary. The lexical system has been initialized with data coming mainly from the conversion of the French-Khmer bilingual dictionary of Denis Richer from Word to XML format. The French part was completed with pronunciation and parts-of-speech coming from the FeM French-english-Malay dictionary. The Khmer headwords noted in IPA in the Richer dictionary were converted to Khmer writing with OpenFST, a finite state transducer tool. The resulting resource is available online for lookup, editing, download and remote programming via a REST API on a Jibiki platform.

Introduction

Economic issues related to the information processing techniques are very important. The development of such technologies is a major asset for developing countries like Cambodia and Laos, and emerging ones like Vietnam, Malaysia and Thailand. The MotAMot project aims to computerize an underresourced language: Khmer. This language is spoken mainly in Cambodia. As indicated by V. Berment in his Ph.D. thesis [START_REF] Berment | Méthodes pour informatiser des langues et des groupes de langues peu dotées[END_REF], "With the development of personal computers and networks, the computer becomes now a tool for writing and communicating in the same way as paper and printing were before. Word processing, email, and even more advanced systems such as dictation or voice synthesis are widely used tools. The idea then is needed than appropriate information technologies tools must be added to traditional means without which the targeted goals can not be achieved any more". The computerization of a language such as Khmer occupies a central place in this wider context. The main goal of the project is the development of a multilingual lexical system targeted for Khmer. The lexical system has been initialized with data coming mainly from the conversion of the French-Khmer bilingual dictionary of Denis Richer from Word to XML format.

Presentation of the resource to be built

Microstructure of the entries

The microstructure of the monolingual volumes is based on the Explanatory and Combinatorial Lexicography.

Each entry is based on the vocable. A vocable is either a group of lexies (word meaning) or an idiom. Each entry consists of a headword and a pronunciation, followed by a list of word meaning (lexies). Each lexie is described either by a lexico-semantic formula (Melcuk & Polguère, 2006 ;[START_REF] Polguère | Structural properties of Lexical Systems: Monolingual and Multilingual Perspectives[END_REF] or a free gloss. For terms, it is possible to describe their domain. Then comes a translation link pointing to an axie (entry) of the pivot volume. It is followed by a list of examples and idiomatic expressions. Finally, a generic field is used to store additional information from reused dictionaries. To cope with different contributor skill levels, the editing interface adapts itself and displays an appropriate granularity of information. For example, a novice contributor will be prompted for a simple gloss to characterize a lexical unit, while an expert linguist will describe a complete semantic formula. Similarly, only specific contributors have access to the list of lexical functions.

Macrostructure of the lexical database

The macrostructure is composed of a monolingual volume for each language and a central pivot volume. However, in order not to confuse users, they contribute through an interface with a classic view of a bilingual dictionary. Each bilingual link language A ➔ language B added via this interface (step 1 in Figure 1) is actually translated into the background by creating two interlingual links as well as an axie link representing the original translation to finally get: language A ➔ pivot axie ➔ language B (step 2 in Figure 1).

If a contributor wants to add a translation link between a vocable Va of language A and a vocable Vb of language B, s/he can establish this link at different levels. The ideal solution is to connect a word meaning (lexie) La of the vocable Va to another word meaning Lb of the vocable Vb. In this case, the link is bijective and Lb is also connected to La (point 1 in Figure 2). If the vocable Vb has not yet defined specific word meanings or if the contributor can not choose between word meanings, s/he can connect directly the word meaning La to the vocable Vb. In this case, a new word meaning Lb is created with a draft level of quality and the link as well as the word meaning are marked for refinement (point 2 in Figure 2).. In the case of reusing existing data, it is often impossible to link information to a specific word meaning. In this case, we add to the end of the vocable Va the information that one of the meanings of vocable Va can be connected to a meaning of vocable Vb but this information will not be added to Vb (point 3 in Figure 2). It will of course be marked as to be refined with emergency! With the pivot macrostructure, if two links language A ➔ language B and language B ➔ language C exist, then it will automatically create a link language A ➔ language C whose level will be marked as a draft and to be revised.

Levels for contributions and contributors

Each information of each entry is assigned a quality level. The levels range from 1 star for a draft (recovered data whose quality is not known) to 5 stars, quality certified by an expert (e.g.: a link translation validated by a sworn translator). Similarly, contributors will be assigned a skill level (1 to 5 stars as well). 1 star is the level of an unknown novice in the community and 5 stars is the level of a recognized expert.

Then, when a level 3 contributor revises a level 2 entry, the entry automatically goes up to level 3. Similarly, if the work of a contributor is systematically validated without corrections by other contributors to the next level, it can automatically switch to the next level after a certain threshold (e.g. 10 contributions).

To go further, we plan to analyse the work of the contributors. If a person contributes massively eg on a particular area, the system will automatically send regular proposals for contribution in the domain.

Preparation of existing data

In order to encourage contributions, it is preferable to provide a skeleton dictionary to modify later rather than an empty dictionary. For each language involved, a list of words of this language will be recovered to create an initial list of entries. It will always be possible to create a new article, but the creations will be subject to verification.

Conversion of a French-Khmer dictionary into XML

Description of the dictionary

For the Khmer language, there is at present a French-Khmer dictionary [START_REF] Richer | Dictionnaire Français-Khmer (en phonétique)[END_REF], which started in the late 90s, was completed in 2006 by a small group of computer scientists gathered in the "Pays Perdu" NPO created by Denis Richer, french ethnolinguist established in Siem Reap (Cambodia). This first version of the dictionary was published in spring 2007 and has 13,249 entries. Each entry is composed by a French headword, in some cases a part-of-speech and a list of word senses.

Each word sense has a gloss in French and a translation in Khmer. The dictionary was originally encoded in Word format. An example of the original file can bee seen on Figure 3.

Conversion of the file into XML

We first converted the dictionary from Word format to a lexical resource in XML format according to the methodology described in (Mangeot & Enguehard, 2013).

The Open Document Format has the great advantage of being based on XML. Instead of a conversion, the contents of the XML document has been retrieved, then transformed to obtain what we want.

A document in ODF format is actually a zip archive containing multiple files including the text content in XML. This content is stored in the "content.xml" file in the archive. To retrieve this file, just follow some clever manipulations. On MacOs, create an empty folder and then copy the .odt file inside. Then, open a terminal and run the "unzip" command to unzip the file. On Windows, you must change the .odt file extension into .zip and then open the. zip archive.

The file "content.xml" can now be extracted from the archive and then renamed and placed in another location.

It becomes the base file on which we will continue our work. The next step consists in editing this file with a "raw" text editor with syntax highlighting and regular expressions based search and replace.

One may first think that since the source file "content.xml" is already in XML, it may be enough to write an XSLT stylesheet to convert the file into an XML dictionary, but the XML used in the source file is completely different from the XML targeted. Indeed, the source file comes from a word processor. It is designed for styling a document and not for structuring a dictionary entry. Therefore, it is finally easier to convert the XML file "by hands" with regular expressions than to write an XSLT stylesheet for automatically converting the source file.

Tagging each part of information

All pieces of information were explicitly tagged by replacing the ODF markup by a new "homemade" tagset. Each piece of information is usually distinguished from others in the original file with a different style. Search/replace operations were performed for each type of information.

The original dictionary file has tow columns. The French is on the left one and the Khmer on the right one. Each entry has one or several word senses. Each word sense is written on one line and has a khmer translation on the right column. Therefore, each line was tagged with "sens" tag (see Figure 4).

the original Word file, feminine forms of adjectives are separated from the masculine with a comma. The feminine form were separated in order to clearly identify the headword of each entry. The original form of the entry is duplicated in the gloss field. The XML file obtained is a unique volume containing French entries translated into Khmer.

Restructuring and links reification

Conversion into the MotÀMot structure

The XML data obtained is then converted into the structure chosen for the MotÀMot project. In files coming from word processors, the data structure is usually implied. New structural elements must be added to move towards a more standardized structure. Concerning standards, Lexical Markup Framework (LMF) [START_REF] Romary | Standards going concrete: from LMF to Morphalou[END_REF]) became an ISO standard in November 2008 [START_REF] Francopoulo | Multilingual resources for NLP in the lexical markup framework (LMF)[END_REF]. It suits ideally our goals. As it is a meta-model and not a format, the principle of the LMF model can be applied to the entry structure and keeping our tags without using the LMF syntax (Enguehard & Mangeot, 2013). The entry tag corresponds to the LexicalEntry object; the head tag corresponds to the Form object; The headword tag corresponds to the Lemma object; the sense tag corresponds to the Sense object; The gloss tag corresponds to the Definition object; the refaxie tag corresponds to the Equivalent object (Figure 6). The core meta-model LMF is shown in Figure 5. Unique identifiers are also added to entries and word senses (Figure 6). They will be used afterwards for linking entries.

Link reification

We then converted this unique volume into three volumes : one French, one pivot and one Khmer by eliciting the translation links. From each French->Khmer translation, we obtain 2 links : one French->Pivot and one Pivot->Khmer. T h e e n t r y fra.abondant.27.e ha s 2 Kh m e r translations: "sɑmbo" & "co ̥ k-coam". They were elicited into the 4 following links:

1 7 shows a French entry after reification. The axi volume is obtained by gathering all the axies in the same file.

The Khmer volume is obtained by gathering all the Khmer entries and by merging them when they have the same Khmer word as headword (at this stage, the comparison is based on the IPA of the Khmer word). Each link to an axie constitutes a sense. The volume will then be sorted by Unicode sort order of the Khmer headword in Khmer writing after the process described in part 4. The French volume contains 13,249 entries; the Khmer volume contains 23,766 khmer entries; the axie volume contains 32,402 axies linking to both a French and a Khmer entry.

Adding data in the French volume

The French entries were enriched with data from the FeM French-English-Malay dictionary : the pronunciation of the headword and the part-of-speech for the nonhomonymous vocables.

Conversion of the IPA in Khmer alphabet

The Khmer part is a simple phonetic transcription of the Khmer translations written in a special API font (SILSophia IPA93) created by the Summer Institute of Linguistics. We developed a program of transcription from the phonetic form to the Khmer writing 1 based on a finite state transducer (FST): OpenFst 2 This program is available online for use at the following URL: http://jibiki.univ-savoie.fr/khmer/ The source code is also available for download from the same page. This work is licensed under the Creative Commons Zero license, public domain.

IPA normalisation

first step is to normalize the IPA notation. It consists in two different parts. The first part is a correction of mistakes in the IPA notation. Some IPA letters that do not 1 http://jibiki.univ-savoie.fr/khmer/ 2 http://www.openfst.org/ The second part is the normalisation of combined letters. In Unicode, some letters with diacritics can be written by combining a basic character with different marks (combining macron, ring below, etc.)

Intermediate notation

During this step, two operations are performed at the same time.

The first one consists in grouping the series of API letters that correspond to one letter in Khmer.

The longest matches are processed before.

The second one consists in tagging the type of syllable. In Khmer, each consonant can be written in two different ways following the composition of the syllable in which the consonant is included. These two variants are considered as two different letters with different Unicode codes. We call the two variants A and B and we tag each consonant with its type.

For tagging the type of consonants, several heuristics are applied in the following order:

In the original file, Khmer words noted in IPA are separated by the '-' character. This feature was used in the conversion when word beginning and endings require special treatments. Some vowels beginning a word like "a" and "ɘ" are specific Khmer letters.

-a -a

-ɘ t -ɘt t -ā -a ā
The consonant "l" ending a word is a type B consonant.

l -l B -

There are three types of vowels:

-some are located after a type A consonant; Next, the consonants are grouped:

c h ch k h kh p h ph t h th

For some consonants followed by third type vowels, it is possible to attribute them automatically a type.

b ūɘ b A ūɘ ch ūɘ ch B ūɘ d ūɘ d A ūɘ t ūɘ t ūɘ b ɯ ̅ ɘ b B ɯ ̅ ɘ k ūɘ k B ūɘ t ɯ ̅ ɘ t B ɯ ̅ ɘ

Khmer generation

The third step consists in generating Khmer writing from the intermediate notation with the two types of consonants.

The vowels are replaced with the same Khmer letters: ɑ̄អ ɯ ̅ ɘ

ឿ

The consonants are replaced following their type:

kh + v + A ខ្ វ kh + v + B

ឃ្ វ

The Khmer language writing system has many ambiguities,. Some letters (most of them word endings) are not pronounced. The result is far from perfect. Nevertheless, it was still added to entries and will then be reviewed by khmer native speakers.

Availability on the Web with the Jibiki platform

Jibiki is a generic platform for manipulating online lexical resources [START_REF] Mangeot | Environnements centralisés et distribués pour lexicographes et lexicologues en contexte multilingue[END_REF] with users and group management, consultation of heterogeneous resources and generic dictionary articles edition. This is a community website originally developed for the Papillon project [START_REF] Mangeot | Construction de données lexicales multilingues, le projet Papillon[END_REF].

Jibiki distinguishes form other lexical resources development platforms such as TshwaneLex from tshwanedje.com, the Dictionary Publishing System from IDM or FieldWork from the SIL on the following points:

-it is completely free and open-source; -it allows to browse and edit any kind of XML lexical resource without modifying the XML structure or tags (so far, more than 100 resources were successfully imported into a Jibiki platform); -it allows to manipulate complex macrostructures such as pivot ones or lexical networks; -it is available online from a simple Web browser; -it is remotely programmable via a REST API.

Description of the platform

The platform is programmed entirely in Java based on the environment "Enhydra". All data is stored in XML format in a database (Postgres). This website mainly offers two services: a unified interface for simultaneous access to many heterogeneous resources (monolingual, bilingual dictionaries multilingual databases, etc...) and a specific editing interface to contribute directly to the dictionaries available on the platform. Several lexical resources construction projects used or still use this platform successfully [START_REF] Mangeot | Dictionary Building with the Jibiki Platform: the GDEF case[END_REF][START_REF] Sérasset | Multilingual legal terminology on the Jibiki platform: the LexALP project[END_REF]. The source code for this platform is published under the LGPL open-source licence and available for free download from the open forge of the LIG laboratory 3 . An instance of the platform has been adapted specifically to the MotÀMot project. The language of the interface is French. It is also envisaged to localize it in Khmer.

Visualisation of Khmer text in browsers

Unfortunately, widespread web browsers based on the Webkit engine such as Safari or Chrome but also word processors such as OpenOffice family are still not able to display correctly all the Khmer letters. Some letters have 3 http://jibiki.ligforge.imag.fr to be composed. The order must change. In the following example, the last letter of the word "jɔn-hɔh" (plane) a dash circle which is in fact an empty placeholder for a vowel. On the same system with the same configuration (MacOs X 10.6.8), Firefox is able to fill in the placeholder (Figure 9) but not Safari (Figure 8).

Volume Lookup

Two different lookup interfaces are available to the user. The volume lookup allows the user to lookup a word or prefix on a specific volume, French or Khmer. The Khmer entries can be searched from their headword in IPA or Khmer writing. On the left part of the result window, the volume headwords are displayed, sorted in alphabetical order. An infinite scroll allows the user to browse the entire volume. On the right part of the window, the entries previously selected on the left part are displayed (see Figure 10).

Advanced lookup

The advanced lookup is available for complex multicriteria queries. For example, it is possible to lookup an entry with a specific part-of-speech, and created by a specific author. On the left part of the result window, the headwords of the matching entries are displayed, sorted in alphabetical order. An infinite scroll allows the user to browse all the matching entries. On the right part, the entries previously selected on the left part are displayed.

Online editing

The editing module is based on an HTML interface model instantiated with the entry to be edited (see Figure 11). The model can be generated automatically from a description of the structure of the entry using an XML schema. It can then be modified to improve the screen rendering. The only information required to publish a dictionary article is the XML schema representing the structure of this entry. In addition, it is possible to edit any type of dictionary provided that it is encoded in XML.

Figure 8 shows the editing interface for the French entry "dictionnaire". The link to the pivot axie is indicated in the refaxie field of the sense block. If a contributor wants to add a new link to a Khmer entry, s/he will use the curved arrow button on the left of the reflexie field in the translation block. Then s/he will be able to look up a word in the Khmer volume. When a Khmer entry is selected, an axie is generated in the background and the appropriate links are added to the French and Khmer entries. The resulting axie link is then shown in the refaxie field of the sense block.

XML data available for download

The XML data of the dictionary (French, Khmer and axies v o l u m e s ) i s a v a i l a b l e f o r d o w n l o a d w i t h a CreativeCommons CC by license via the "Données" tab on the MotÀMot website. Data exports from the database will be regularly performed and the new versions available for download.

Remote access via a REST API

Once dictionaries are uploaded into the Jibiki server, they can be accessed via a REST API 4 . Lookup commands are 4 http://jibiki.univ-savoie.fr/motamot/Api.po available for querying indexed information: headword, pronunciation, part-of-speech, domain, example, idiom, etc. (see Figure 12). The API can also be used for editing entries provided that the user previously registered in the website.

Conclusion

The MotÀMot project has now ended. The project website is available at the following URL: http://jibiki.univ-savoie.fr/motamot/ Users can lookup and edit French and Khmer dictionary entries. They can also download the resulting XML data. The platform can be used remotely from other applications via a REST API. The quality of the data can be increased subsequently. Particularly the Khmer entries and headwords that were generated automatically need revision by Khmer native speakers. Of course, people can already voluntarily contribute, but it is very difficult to do so without at least a community manager that can help and motivate contributors. We are now looking for funds in order to found a second project focused on the data revision.

Figure 1 :

 1 Figure 1: Building bilingual links

Figure 3 :

 3 Figure 3: Extract of the dictionary in Word format

  <m:entry id="fra.abondant.27.e" level=""> <m:head> <m:headword>abondant</m:headword> <m:pronunciation>ABON-DAN-</m:pronunciation> <m:pos>adj.</m:pos> <m:fem_form>abondante</m:fem_form> <m:fem_pron>ABON-DAN-T</m:fem_pron> </m:head> <m:sense id="s1" level=""> <m:gloss>abondant, e (fruits, riz…)</m:gloss> <m:refaxie idrefaxie="axi.[fra:abondant, khm:sɑmbo].27.1.e" /> </m:sense>

Figure 5 :Figure 6 :

 56 Figure 5: LMF core metamodel

Figure 10 :Figure 9 :

 109 Figure 10 : Entry "dictionnaire" of the French-Khmer dictionary in Jibiki

  . Sense s1 of French entry fra.abondant.27.e linked to Axi entry

	axi.
	[fra:abondant,khm:sɑmbo].27.1.e;
	2. Axi entry axi.
	[fra:abondant,khm:sɑmbo].27.1.e
	linked to Khmer entry sɑmbo;
	3. Sense s2 of French entry
	fra.abondant.27.e linked to Axi entry
	axi.[fra:abondant,khm:co ̥ k-
	coam].27.2.e;
	4. Axi entry axi.[fra:abondant,khm:co ̥ k-
	coam].27.2.e linked to Khmer entry co ̥ k-
	coam.
	Figure

Table 1 :

 1 replacement operations for API normalisation

			but also exist in one
	global character. When one character exists, the
	combining characters where replaced by the equivalent
	global character.
	Original	Replacement
		Corrections
	y		j
	f		hv
	n		ŋ
	Normalisations
	a +	̄ā
	o + ̄ + ̥	ō̥

Acknowledgements

The MotÀMot project has been partly funded by the Agence Universitaire de la Francophonie. We also thank Vanra IENG for his work on the project.