Romain Marteau
email: romain.marteau@ubourgogne.fr

Vincent Moron

Nathalie Philippon

Spatial coherence of monsoon onset over Western and Central

HAL is

Introduction

The rainy season over the Sahelian belt spans only few months, mainly from July to September [START_REF] Lamb | Case studies of tropical Atlantic surface circulation patterns associated with subsaharan weather anomalies: 1967 and 1968[END_REF][START_REF] Nicholson | Revised rainfall series for the WestAfrican subtropics[END_REF][START_REF] Nicholson | The nature of rainfall fluctuations in subtropical Africa[END_REF], and is associated with the latitudinal shift of the whole monsoon system. Previous work has shown that the northward shift, which determines the largescale onset of the rainy season across the Sudanian and Sahelian belts, usually occurs at the end of June, as an abrupt jump between Guinean (i.e. 5°8°N) to Sahelian (i.e. 10°14°N) latitudes (Sultan andJanicot 2000, 2003;Sultan et al. 2003;[START_REF] Fontaine | SudanSahel rainfall onset : definition of an objective index, types of years, and experimental hindcast[END_REF]. The monsoon withdrawal in late September over the Sahelian belt is much smoother [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF]. "Preonset" scattered rains could occur over the Sahelian belt before the large scale SN jump, while most of the Sahelian seasonal rainfall are associated with westward moving squalllines (SLs) of mean horizontal extent of ~ 500 km and propagation speed of 10 15 m/s (i.e. [START_REF] Martin | Characteristics of West African and east Atlantic cloud clusters: a survey from GATE[END_REF][START_REF] D'amato | on the characteristics of the rainfall events in the Sahel with a view to the analysis of climatic variability[END_REF][START_REF] Laurent | How important is the contribution of the Mesoscale Convective Complexes to the Sahelian rainfall?[END_REF][START_REF] Mathon | Mesoscale convective system rainfall in the Sahel[END_REF].

The timing of the start of the rainy season is crucial to decide when to plant crops [START_REF] Sivakumar | Empirical analysis of dry spells for agricultural applications in West Africa[END_REF]. This is of particular importance for the Sahelian belt where economy is mostly based on rainfed agriculture, with weak capacity to mitigate adverse effects of interannual variability of rainfall [START_REF] Ingram | Opportunities and constraints for farmers of west Africa to use seasonal precipitation forecasts with BurkinaFaso as a case study[END_REF]. In that context, any reliable prediction of the localscale onset date would be of a great value to assist on time preparation of farmlands, mobilisation of seed, manpower and equipment, and would also reduce the risks of planting at an unfavorable time [START_REF] Omotosho | Predicting monthly and seasonal rainfall, onset and cessation of the rainy season in West Africa using only surface data[END_REF]. [START_REF] Sultan | Agricultural impacts of 2 the largescale variability of the West African monsoon[END_REF] clearly demonstrated that the "ideal" sowing date, i.e. the one leading to the highest yields, is close to the largescale onset date, defined as the northward jump of the Intertropical Convergence Zone (ITCZ).

The definition of the onset of the rainy season over West Africa has generally followed two approaches: (i) a localscale one and (ii) a largescale one. Methods for detecting the onset of the rainy season at localscale have been proposed as early as the 70's for specific Sahelian settings (in Niger mainly, [START_REF] Davey | An evaluation of climate and water resources for the development of agriculture in the SoudanoSaelian zone of West Africa[END_REF][START_REF] Benoit | The start of the growing season in Northern Nigeria[END_REF]. Most methods rely on insitu daily measurements of rainfall meeting subjective thresholds [START_REF] Davey | An evaluation of climate and water resources for the development of agriculture in the SoudanoSaelian zone of West Africa[END_REF][START_REF] Stern | The start of the rains in West Africa[END_REF][START_REF] Sivakumar | Predicting rainy season potential from the onset of rains in southern sahelian and sudanian climatic zones of West Africa[END_REF][START_REF] Jolliffe | Early detection of the start of the wet season in tropical climates[END_REF][START_REF] Balme | Démarrage de la saison des pluies au Sahel : variabilité aux échelles hydrologique et agronomique, analysée à partir des données EPSATNiger[END_REF]. These empirical thresholds are chosen according to the climatological properties of the rainy season as well as agronomic criteria (these points will be detailed in section 3). In this approach, the onset is primarily assumed as a change in the properties, frequency and/or intensity of rainfall events associated with the arrival of the monsoon air mass. Other parameters have also been taken into consideration to detect local onsets, such as evapotranspiration [START_REF] Benoit | The start of the growing season in Northern Nigeria[END_REF][START_REF] Ati | A comparison of methods to determine the onset of the growing season in Northern Nigeria[END_REF].

A more recent largescale approach is based on subcontinental indexes of observed rainfall or rainfall proxies such as outgoing long wave radiation (OLR) [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF]. The seasonal cycles of pentad rainfall averaged over West African longitudes (e.g. 10°W10°E)

show an alternation of steep increases and pauses [START_REF] Louvet | Active phases and pauses during the installation of the West African monsoon through 5day CMAP rainfall data (1979[END_REF] during its northward progression. One of these pulses appears to be associated with the abrupt northward shift of the ITCZ, the socalled "ITCZ jump" [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF]. The onset is thus only defined from the planetaryscale northward shift of the monsoon, and a single date is given for a given band of longitudes.

The approach of [START_REF] Camberlin | Application of daily rainfall principal component analysis to the assessment of rainy season characteristics in Senegal[END_REF] can be viewed as an intermediate approach. In their study, an Empirical Orthogonal Function (EOF) analysis is applied to localscale, daily rainfall anomalies in Senegal for a multiyear period. A single onset date was then computed for the whole country as the minimum of the cumulative sum of the leading principal component (PC) time series on a yearly basis. This date is representative of the localscale onset dates for the stations highly correlated with the leading PC, and part of localscale interstation noise is filtered out through the spatial weighting provided by the EOF. The localscale definition is clearly the most suitable for endusers so that they can use the information as a valuable decisionmaking parameter. In that context, three important related questions are explored in this paper:

1. How pertinent is the localscale definition, proposed in previous studies for specific settings across the Sahel, for a larger longitudinal belt? The previous definitions are based on subjective thresholds chosen according to climatological and/or agronomic features. The sensitivity of the onset date (in terms of mean and interannual variability) to this parametrization has never been evaluated.

2.

To what extent do the average and localscale onset date match with the regional scale (i.e. as defined by [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF] ones? Is the abrupt jump of the ITCZ noticeable across the network? These issues are related to the shape and intensity of potential modes of variability of onset date. They are also intrinsically related to the intensity of the spatial coherence and potential predictability of onset date.

3. The spatial coherence of a phenomenon is partly indicative of its potential predictability: It is indeed expected that global or regionalscale sea surface temperatures anomalies should induce a rather smooth, roughly spatiallyuniform, anomalous signal at regionalscale, at least for a flat area such as the Sahel [START_REF] Moron | Seasonal predictability and spatial coherence of rainfall characteristics in the tropical setting of Senegal[END_REF][START_REF] Moron | Spatial coherence of tropical rainfall at the regional scale[END_REF]. As forecasts of the rainy season onset is desired by user communities, an estimate of its potential predicatbility is a first step toward this goal.

These three issues are analyzed from a 103 raingauge network covering Western and Central Sahel (Senegal, Mali and BurkinaFaso) from 1950 to 2000. Section 2 describes the different daily rainfall datasets. Section 3 provides the main results in terms of (i) definition of the local scale onset date, (ii) climatological mean and characteristics of the rainfall field before and after the onset, (iii) interannual variability and spatial coherence of onset date. Conclusions are given in section 4.

Daily rainfall data

The daily rainfall analysed in this study come from two different databases: Daily rainfall amounts recorded at 29 stations come from the Senegal DMN. Most of the stations are located in the western part of the country while the eastern part is less sampled (Fig. 1).

b. Filling the missing values

Missing daily rainfall observations (less than 3%) were replaced with a local scaling [START_REF] Widmann | Statistical precipitation downscaling over the Northwestern United States using numerically simulated precipitation as a predictor[END_REF][START_REF] Ines | Bias correction of daily GCM outputs for crop simulation studies[END_REF][START_REF] Schmidli | Downscalling from GCM precipitation : a benchmark for dynamical and statistical downscalling methods[END_REF]) of daily ERA40 rainfall. For each station, the closest ERA40 grid point is chosen, and its daily rainfall is scaled so that the frequency of occurrence of wet day > 1 mm and the mean intensity of daily rainfall during wet days match the longterm monthly mean of the available data. Missing entries are then replaced by the calibrated ERA40 rainfall for these particular days. Note that replacing the missing entries from May to October with a simple stochastic weather generator [START_REF] Wilks | Interannual variability and extremevalue characteristics of several stochastic daily precipitation models[END_REF]) leads to very similar results.

Results

a. Agronomic definition of onset

The localscale agronomic definition of the onset is the most relevant to agriculture management. This definition is based on localscale daily rainfall using empirical thresholds of rainfall that ensure enough soil moisture during planting and growing periods to avoid crop failure [START_REF] Walter | Length of rainy season in Nigeria[END_REF][START_REF] Omotosho | Onset of thunderstorms and precipitation over northern Nigeria[END_REF][START_REF] Omotosho | Longrange prediction of the onset and end of the rainy season in the West African Sahel[END_REF][START_REF] Omotosho | Predicting monthly and seasonal rainfall, onset and cessation of the rainy season in West Africa using only surface data[END_REF]. Table 1 lists the different thresholds used in selected previous studies dedicated to the Sahelian domain. Most of the studies agree on two criteria; (i) 1 or 2 consecutive days receiving at least 2025 mm of rainfall, and (ii) no 7day dry spell in the following 30 days from the onset. The threshold of 20 mm amount was adopted following a study by ICRISAT dedicated to millet in Niger [START_REF] Davey | An evaluation of climate and water resources for the development of agriculture in the SoudanoSaelian zone of West Africa[END_REF][START_REF] Sivakumar | Empirical analysis of dry spells for agricultural applications in West Africa[END_REF]) and corresponds to the minimum water requirement for crop survival.

Considering at least 2 consecutive days is a reasonable choice to take into account a rain event that occurs across the recording time (usually between 7 and 9 a.m local time). In fact, SLs develop themselves mainly in late afternoon and persist sometimes during the night [START_REF] Martin | Characteristics of West African and east Atlantic cloud clusters: a survey from GATE[END_REF]. The 7day dry spell after the onset is known as the "control period" and prevents against "false" onsets that have disastrous consequences on germination and crop development [START_REF] Sivakumar | Empirical analysis of dry spells for agricultural applications in West Africa[END_REF], and require farmers to sow again while the seed's stock is usually small [START_REF] Diop | A propos de la durée de la saison des pluies au Sénégal[END_REF]. Moreover, anything less than 50 percent of the weekly crop water requirement (CWR) will likely lead to crop failure (i.e. [START_REF] Omotosho | Predicting monthly and seasonal rainfall, onset and cessation of the rainy season in West Africa using only surface data[END_REF]. The CWR equals at least 10 mm across the Sahel, leading to a threshold of 5 mm in 7 days to define a dangerous limit for crop survival after the first rains.

In the current study, a wet (dry) day is defined as a day receiving more (less) than 1 mm [START_REF] Diop | Caractérisation du facteur hydrique en agriculture pluviale au Sénégal: le cas de l'arachide et du mil[END_REF]) because (i) rainfall amounts between 0 and 1 mm are not equally reported across countries and stations (i.e. synoptic or not), and (ii) considering daily amounts less than 1 mm usually increases the interstation noise [START_REF] Moron | Spatial coherence of tropical rainfall at the regional scale[END_REF]) when determining onset. The onset date (OD hereafter) is defined here as the first wet day of 1 or 2 consecutive days receiving at least 20 mm without any 7day dry spell receiving less than 5 mm during the following 20 days 9 counted from the onset. OD is computed from May, 1 st . These criteria are obviously too restrictive for the driest stations and years. While less than 0.4% of stationyear do not experience any 2day receiving at least 20 mm during MayNovember season, 8.6% of onset are undefined when the postonset 7day dry spell receiving less than 5 mm in the following 20 days is included in the definition. This percentage reaches 19% when the control period length is extended to 30 days from the initial wet spell. A window of 20day is thus retained as a compromise between the need to consider "false" starts and a too restrictive threshold that excludes many stations and years. Undefined onset dates still account for 40% of years for the 14 stations north of 15°N. In most of these cases, no rainy season is actually experienced with scattered rainy events spread across the season. In the following analyses (except for EOF in section 3d), the undefined onset dates (8.6%) are replaced by the latest available onset date observed across the network for the given year, weakly increasing the spatial coherence over the northern edge of the domain.

Figure 2a displays the mean onset dates averaged over the 51 years. The mean OD exhibits a rather regular northward shift , mixed with a secondary northwestward one over Senegal, from mid May (south Burkina Faso) to early August (NW Senegal and centralnorthern Mali).

Respectively, 17.9%, 31.4%, 36.1% and 12.7% of onset occur in May, June, July and August (Fig. 2b).

b. Mean characteristics of rainfall field before and after the onset 1 Figure 3 shows the mean characteristics of the rainfall field averaged over the 15 days before and 15 days after the localscale OD. These periods are extracted for each station on a yearly basis, and the frequencies of occurrence of wet days receiving respectively between 1 and 20 mm and > 20 mm are computed (Fig. 3ad) as well as the mean length of the wet and dry spells (Fig. 3eh).

Before the onset, the frequency of occurrence of wet days receiving between 1 and 20 mm is far from zero (usually 1020%). By contrast, the frequency of occurrence of wet days receiving > 20 mm is very low (14%), but this is almost fully explained by the criteria used to define OD (see section 3a). The mean dry spell length is rather homogeneous, usually between 4 and 6 days, without any clear northward increase (Fig. 3g). Similarly, the mean wetspell length is rather spatially uniform, between 1 and 2 days, still without any clear northward decrease (Fig. 3e).

From the onset, the frequency of occurrence of wet day receiving between 1 and 20 mm increases smoothly, by a factor of 2, while the frequency of occurrence of wet day > 20 mm is roughly multiplied by 5. The multiplication of wet days breaks up the dry spells, that are consistently shorter than before the onset (less than 3 days except for several northern stations, Fig. 3g,h) while the mean wet spell length remains shorter than 2 days (Fig. 3i,j). In other terms, at localscale, the onset is usually associated with more and wetter rainy days afterwards, but those wet days remain rather isolated or clustered into 2day wet sequences. This could be 1 related to the dominant influence of SLs and the usual scarcity of longlasting wet spells at these latitudes.

Figure 4 further illustrates the relative rainfall field near the onset date, in particular its spatial pattern. For each station and each year, the frequency of occurrence of daily rainfall > 1 mm for 2 days before (Fig. 4a), and after (Fig. 4b) the localscale onset (and their difference, Fig. 4c) is computed for the whole rainfall field relocated relative to the reference station (i.e. (0,0) location on Fig. 4). In other words, Figures 4b,c illustrate the spatial coherence of the "first kind", i.e. the frequency of occurrence of a wet day around a station when its onset occurs.

Figure 4a is roughly similar to the mean climatological pattern of frequency of occurrence, i.e. a northward gradient, also visible in the mean onset date (Fig. 2). Considering the longterm mean of the frequency of occurrence of any other sample of 2 days leads roughly to the same pattern, except that the spatial mean varies according to the seasonal cycle of rainfall (not shown). The occurrence of localscale OD slightly alters this pattern (Fig. 4b), mostly through an increase of the frequency of occurrence of an elongated WSWENE shape around the reference station (Fig. 4c). A small asymmetric surface of 3°4° (~ 1°) in longitude by 2° (~ 1°) in latitude around the reference station exhibits significant (at the twosided 90% level according to a Student's T test) increase of the frequency of occurrence for 75% (90%) of the time between pre and postonset 2 days (Fig. 4c). Thus, figure 4 suggests that localscale OD seems hardly related to coherent spacetime propagating features at meso or synopticscale and/or even the planetaryscale because neither regular northward (possibly associated with an 1 abrupt jump of the ITCZ), nor westward (possibly associated with a SL) progression appears between panel (a) and (b) of Figure 4. Increasing the length of the time period averaged before and after the onset to 5, 10, 20 and 30 days is associated with a wider ~ WE belt of increased frequency of occurrence of rainfall, probably in relation with the mean northward shift of the overall rain belt, especially for periods lasting at least 10 days (not shown).

c. Spatial coherence of the onset date at interannual time scale

The spatial coherence of the "second kind" is the possible systematic modulation of onset dates (or any other seasonal characteristic) at interannual time scale. Note that a weak spatial coherence of the "first kind" (section 3b) does not necessarily forbid this effect because a large scale forcing could synchronize the onset dates in time, by systematically delaying or bringing forward the onset of the rainy season at localscale [START_REF] Moron | Spatial coherence and seasonal predictability of monsoon onset over Indonesia[END_REF]. The spatial coherence of the OD at interannual time scale has been estimated through degrees of freedom (DOF) [START_REF] Moron | Guinean and Sahelien rainfall anomaly indices at annual and monthly scales (19331990)[END_REF][START_REF] Fraedrich | Estimates of spatial degrees of freedom[END_REF][START_REF] Bretherton | The effective number of degrees of freedom of a time varying field[END_REF][START_REF] Moron | Seasonal predictability and spatial coherence of rainfall characteristics in the tropical setting of Senegal[END_REF]) and interannual variance of the standardized anomaly index (SAI) (var[SAI]) [START_REF] Katz | Anatomy of a rainfall index[END_REF]. The DOF are computed following the equation of [START_REF] Fraedrich | Estimates of spatial degrees of freedom[END_REF]:

2 1 ² M i i M DOF e = = ∑
where M is the number of stations and e, the eigenvalues of the correlation matrix. The DOF varies between 1 and the rank of the correlation matrix. In the limiting case of e i = 1 for all 1 orders, DOF = M, that is, each station conveys independent information and the common "signal" is zero. On the other hand, if the first eigenvalue accounts for all variance of the field, then DOF = 1, that is, each station conveys the same information equal to the signal and the noise is zero. Note that due to finite length, the highest DOF expected for a 51 x 103 matrix of independent white noise is not 50, but rather ~ 34. The var [SAI] ranges between 0 (correlation of 1 between two equalsized and perfectly outofphase samples), 1/M (~ 0.01 in our case, for spatially independent variations), and 1 (perfect correlation between stations) [START_REF] Moron | Seasonal predictability and spatial coherence of rainfall characteristics in the tropical setting of Senegal[END_REF][START_REF] Moron | Spatial coherence of tropical rainfall at the regional scale[END_REF].

Here the DOF of the localscale OD is high (23.7) indicating a weak spatial coherence at the regional scale. The var[SAI] equals 0.07 and is also close to the value associated with a white noise time series. For comparison, the DOF and var[SAI] equal 6.1 (respectively 4.8) and 0.36 (respectively 0.41) for the MayNovember seasonal rainfall amounts (respectively frequency of occurrence of wet days > 1 mm). Therefore, according to DOF and var[SAI], the agronomic OD is characterized by a considerable amount of interstation noise, and in consequence, is assumed to be poorly predictable from largescale predictors at the interannual time scale [START_REF] Moron | Seasonal predictability and spatial coherence of rainfall characteristics in the tropical setting of Senegal[END_REF][START_REF] Moron | Spatial coherence of tropical rainfall at the regional scale[END_REF]. To test the sensitivity of the spatial coherence to parametrization, (respectively 0.6). The impact of the length of the control dry spell (L d ) was also tested with A w and L w set to 20 mm and 2 days respectively, while L d was set equal to 5, 7, 9, 11, 13, and 15 days in the 20 days from the onset. Note that undefined onsets decrease almost exponentially from 25% to 1% between the extreme values of L d . DOF and var [SAI] are almost stable between 25 and 26 and < 0.10 respectively. In summary, the weak spatial coherence of "second kind" is not related to the parametrization of the OD.

d. Interannual to interdecadal variability of the onset date

To further examine the interannual variability of OD, an Empirical Orthogonal Function (EOF) analysis based on its correlation matrix is computed. Note that undefined onsets are left untouched here and that correlation matrix is computed only from pairs of available ODs. The leading EOF mode of OD accounts for 8.7% of the total variance consistently with the weak spatial coherence depicted above. By contrast, the leading EOF of the MaySeptember seasonal amount (the frequency of occurrence of wet days > 1 mm) accounts for 38.1% (respectively 43.4%) of the total variance. The second unrotated EOF mode of onset date explains less than 6.4% of total variance. The first unrotated mode (Fig. 5a) describes a relatively coherent structure of OD variability mostly over Western and Central Senegal. This behaviour could be at least partly related to the relatively high spatial sampling (Fig. 1), but could be also related to a slightly stronger signal [START_REF] Camberlin | Application of daily rainfall principal component analysis to the assessment of rainy season characteristics in Senegal[END_REF]. The corresponding leading EOFs of seasonal amount (Fig. 5b) and frequency of occurrence of wet days > 1 mm (Fig. 5c) exhibit larger scale patterns with loadings > 0.6 spread all across the domain without a clear spatial gradient. The leading PC of onset date (respectively seasonal amount and frequency of occurrence) (Fig. 5d) exhibits a positive (negative) and statistically significant (at onesided 95% confidence level) trend, i.e. a delayed onset (decreased seasonal rainfall and frequency of occurrence) from 19502000. The median of localscale correlations between onset on one hand and seasonal amount and frequency of occurrence on the other hand equals only 0.35.

1

In order to analyse the relationships between the localscale and the regionalscale onset date as defined by [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF] through the SN jump of the ITCZ the localscale OD are extracted from 1968 (available online at http://www.lodyc.jussieu.fr/~bslod/monsoon.htm).

Note that DOF of localscale OD for the 19682000 period equals ~19, but this apparent higher spatial coherence could be an artefact of the decrease of the matrix rank from 50 to 32. The correlations between the largescale and the 103 localscale ODs are between 0.54 and 0.41, with only 7 values being significant at the twosided 95% level according to a random phase test [START_REF] Janicot | Sahel drought and ENSO dynamics[END_REF]. Moreover, the correlation between regionalscale OD as defined by [START_REF] Sultan | Abrupt shift of the ITCZ over West Africa and intraseasonal variability[END_REF] and a regional index (SAI) or the leading PC of onset date equals only 0.06 and 0.24 (both values are not significant at the twosided 90% level). The largescale onset is divided in 3 terciles of early (1969, 1982, 1985, 1973, 1978, 1994, 1996, 1999, 1993, 1974, 1977), nearnormal (1990, 1992, 1975, 1980, 1970, 1983, 1986, 1968, 1976, 1971, 1979) and late (1981,1972,2000,1985,1988,1997,1984,1989,1987,1998,1991) jumps of the ITCZ. The localscale OD anomalies are then averaged for the three sets of years. There is a considerable amount of interstation noise for each of the terciles and the number of stations where the OD anomaly is significantly different from zero (based on a onesided ttest at the 90% confidence level) is always less than 15% (not shown).

Lastly, the teleconnections between local scale OD and four sea surface temperature (SST) indices, capturing ocean sectors known for exerting an influence over West African Monsoon were considered (i.e. [START_REF] Nicholson | The quasiperiodic behavior of rainfall variability in Africa and its relationship to the Southern Oscillation[END_REF][START_REF] Ropelewski | Global and regional scale precipitations associated with El Niño/Southern Oscillation[END_REF][START_REF] Rowell | Variability of summer rainfall over tropical North Africa (19061992): Observations and modelling[END_REF]1 Nicholson and Kim 1997;[START_REF] Janicot | Sahel drought and ENSO dynamics[END_REF][START_REF] Janicot | Summer SahelENSO teleconnection and decadal time scale SST variations[END_REF]. These indices include the east equatorial Pacific (NINO3.4, 170°W120°W; 5°S5°N), the North Tropical Atlantic (NATL: 60°W30°W; 5°N20°N), the South Tropical Atlantic (SATL: 30°W10°E; 0°20°S) and the Guinean Gulf (GGUI: 10°W10°E; 5°S5°N). Figure 6 displays distribution of correlation coefficients between localscale OD and each SST indices averaged over MayJuly (i.e. including ~85% of the localscale onset, Fig. 1) for 19502000, 19501969 and 19702000. At least 50% of correlation coefficients are between 0.2 and +0.2 and the significant value are usually scattered in space (not shown). In summary, the teleconnections between the SST related to the ENSO phenomenon, the Tropical Atlantic dipole, or Guinea Gulf and localscale OD seem weak.

Conclusion

The main goal of this paper was to analyze the spatial coherence, robustness and the interannual variability of the localscale onset date (OD) of the boreal summer monsoon over Western and Central Sahel (Mali, BurkinaFaso, Senegal) from a network of 103 rain gauges (Fig. 1) with almost complete records from 1950 to 2000. The localscale OD is first defined as the first wet day > 1 mm of one or two consecutive day receiving at least 20 mm without any 7day dry spell receiving less than 5 mm in the following 20 days from the onset. This localscale definition follows previous studies [START_REF] Stern | The start of the rains in West Africa[END_REF][START_REF] Sivakumar | Predicting rainy season potential from the onset of rains in southern sahelian and sudanian climatic zones of West Africa[END_REF][START_REF] Omotosho | Onset of thunderstorms and precipitation over northern Nigeria[END_REF][START_REF] Jolliffe | Early detection of the start of the wet season in tropical climates[END_REF][START_REF] Omotosho | Predicting monthly and seasonal rainfall, onset and cessation of the rainy season in West Africa using only surface data[END_REF][START_REF] Dodd | Early detection of the start of the wet season in semiarid tropical climates of western Africa[END_REF] and is best suited for end user purposes since it explicitly takes into account the rainfall demand for crop seeding and survival during the first stages of growth. This analysis complements previous similar studies 1 (summarized in Table 1) which typically considered a smaller subset of stations and did not deeply investigate the sensitivity of the mean OD and its variability related to the subjective parameters used in its definition such as the length and amplitude of the initial wet spell.

The spatial coherence of OD is analyzed from two points of view: (i) a quasiinstantaneous pattern of rainfall when onset date occurs at a particular station (Fig. 4) and (ii) the synchronization of onset dates at interannual time scale, i.e. the possible systematic modulation of onset dates across the Sahelian band (Fig. 5). The spatial coherence of the "first kind" exhibits a small, significant increase of frequency of occurrence of rainfall relative to preonset 2day (Fig. 4c). This could be associated with a range of factors, from convective cells to meso convective clusters that probably trigger the localscale onset. The spatial coherence of the "second kind" is analyzed through empirical estimates of the degrees of freedom (DOF) or interannual variance of the Standardized Anomaly Index (var[SAI]). Both estimates suggest a weak spatial coherence, i.e. the onset date is hardly systematically synchronized at interannual time scales. This is also demonstrated by the weak amount of variance accounted for by the leading EOF (Fig. 5a). These results contrast with the seasonal amount and the frequency of occurrence which exhibit a largescale pattern across the whole belt analyzed (Fig. 5b,c). The weak spatial coherence of the "second kind" is almost independent of the parametrizations used in the definition of the onset date.

1

These suggest that largescale potential forcing seems unable to systematically synchronize the occurrence of the first rains above a fixed threshold across the western and central Sahel. The occurrence of the localscale onset could be hardly viewed as a systematic event across year and station, but merely a complex product of the multiscale phenomena that produce rainfall over this area. The discrepancy between the localscale OD defined here and the regionalscale onset defined by the northward jump of the monsoon is especially puzzling and needs further investigation. It is possible that localscale onset as defined here could be associated either with a localized convective event, even before the SN jump of the ITCZ, or with a mesoscale squall line. But even in this latter case, the timing of occurrence, size, location and track of the first squall line of the rainy season are hardly reproducible from one year to the next. In other words, there are too many different phenomena, or different scales of motion, that could lead to 540 mm rainy event in 210 days at localscale. If the northward jump of the monsoon enhances the probability of such events across the Sahel, the fact that ITCZ has moved to its northernmost seasonal location, does not necessarily induce localscale onset everywhere at the same moment or even on a short time step.

An important consequence is that localscale OD appears to show little potential predictability based on large and regionalscale boundary conditions such as sea surface temperatures and/or soil moisture [START_REF] Folland | Sahel rainfall and worldwide sea temperatures[END_REF][START_REF] Philippon | The relationship between the Sahelian and previous 2nd Guinean rainy seasons: a monsoon regulation by soil wetness ?[END_REF][START_REF] Douville | Soil moisture memory and West African monsoon predictability: artefact or reality?[END_REF]. This is because the regionalscale seasonal potential predictability implies that the variable of interest shares a variable, but significant, amount of common or covariant information at this scale, at 2 least for a flat area as Sahel. The fact that seasonal rainfall amount and frequency of occurrence are far more spatiallycoherent than the onset date (i.e. DOF equals respectively 6.1, 4.8, and 2328) suggests that most of the seasonal predictability of rainfall over the Sahelian belt is actually not associated with a systematic delay or advance of the localscale onset as defined here, but stands out for example as a seasonallyvarying or constant systematic modulation of the frequency of occurrence of rainfall across the season [START_REF] Moron | Spatial coherence of tropical rainfall at the regional scale[END_REF]. This is not a trivial result, because localscale onset sometimes conveys a spatiallyconsistent signal and potential predictability, as in Indonesia [START_REF] Moron | Spatial coherence and seasonal predictability of monsoon onset over Indonesia[END_REF]. This analysis emphasizes also the need to carefully examine the context of any localscale analysis of the onset, because the weak spatial coherence implies a potential large uncertainty due to random sampling. More work is also needed to look at other definitions of the onset, for example integrating the daily rainfall in time and/or in space. The spatial noise is not necessarily evenly distributed across the scales and it would be interesting to look at intermediate scales between the localscale and largescale onsets. In particular, any definition that filters out some of the localscale noise as the cumulative daily rainfall anomalies [START_REF] Camberlin | Application of daily rainfall principal component analysis to the assessment of rainy season characteristics in Senegal[END_REF]Liebmann et al. 2007) is especially appealing in this context. The apparent spatial increase of the signal over Western and Central Senegal (Fig. 5a) warrants also further studies.

Figures captions

Figure 1: Location of the 103 Sahelian raingauge used in this study. Table 1. Criteria of the agronomic definitions of the localscale onset date of the rainy season used in selected previous studies. All of these definitions start from daily rainfall observed at raingauge stations. the number of localscale correlations significant at twosided 95% confidence level according to a random phase test [START_REF] Janicot | Sahel drought and ENSO dynamics[END_REF].

  demonstrates that at least two different strategies are used to define the onset.

  (i) the FRIEND AOC (Flow Regimes from International Experimental and Network Data Afrique de l'Ouest et Centrale) group (http://armspark.msem.univmontp2.fr/FRIENDAOC/), and (ii) the Senegalese DMN (Direction de la Météorologie Nationale) that provided us with in situ daily data of 103 stations for the period 1950 to 2000 (Fig. 1). a. Rainfall data Data for 33 stations in Mali and 41 stations in BurkinaFaso were compiled by the FRIEND AOC group from various sources (IRD -Institut de Recherche pour le Développement -, ASECNA -Agence pour la SECurité de la Navigation Aérienne en Afrique -, DMN -Direction Météorologique Nationale -and CIEH -Comité InterAfricain d'Etudes Hydrauliques -).

  DOF and var[SAI] have been computed again, by changing (i) the length of initial wet spell (L w = 2 to 10 days) and (ii) the amount of rainfall received during the initial wet spell (A w= 1, 5, 10, 15, 20, 25, 30, 35 and 40 mm) while the other criterion (i.e. a 7day dry spell receiving less than 5 mm in the following 20 days) is kept fixed. Note that the percentage of undefined onset 1 dates is always < 10% in mean, except when A w > 25 mm and L w < 4 days (maximum of undefined onset = 19.1% for A w = 40 and L w = 2). As before, the missing entries are replaced by the latest interannual onset date, slightly increasing the spatial coherence on the northern edges.DOF and var[SAI] are indeed very stable amongst the 81 different estimates; DOF varies between ~23 and ~28 with 88% of values between 23 and 25 and var[SAI] varies between 0.065 and 0.086. In other words, increasing the length and/or amplitude of the initial wet spell has a very weak impact on the spatial coherence. Even the climatological longterm mean and the interannual variability at localscale are only weakly sensitive to the parametrization of A w and L w.. 52% (respectively 76%) of the localscale mean bias between two different estimates of OD are less than 5 days (respectively 10 days) in absolute value and 77% (respectively 88%) of the localscale correlations between two different estimates of OD are equal or greater than 0.7

Figure 2 :Figure 3 :

 23 Figure 2: (a) Climatological (19502000) localscale onset date (b) distribution of cumulative

Figure 4 :

 4 Figure 4: Mean frequency of occurrence of daily rainfall > 1 mm for 2day before (a) and from

Figure 5 :

 5 Figure 5: (a) Leading unrotated empirical orthogonal function (EOF) modes of the localscale

Figure 2 :

 2 Figure 2 : (a) Climatological (19502000) localscale onset date (b) distribution of cumulative frequency of the local onset date (25, 50 and 75 percentiles are indicated by vertical dashed line).

Figure 3 .

 3 Figure 3. Rainfall field statistics averaged over the 15 days before (left column) and from (right column) the localscale onset date. Mean frequency of occurrence (× 100) of wet days receiving between 1 and 20 mm (a, c) and > 20 mm (b, d). Mean wet spell length (e, f) and dry spell length (g, h) in tenth of day.

Figure 4 .

 4 Figure 4. Mean frequency of occurrence of daily rainfall > 1 mm for 2day before (a) and from (b) the localscale onset, and the "(b) minus (a)" difference (c). All fields are relocated relatively to the base station (coordinates = 0,0). In the latter panel, the simple (double) circles indicate a relative location where 75% (90%) of the difference (b)(a) are significant at the two sided 90% level according to a Student's T test.

Figure 6 :

 6 Figure 6 : Boxplot of correlation coefficients between localscale onset date and NINO3.4, Tropical Atlantic dipole and Guinea gulf SST index for periods19502000, 19501969 and 19702000. Boxes are bounded by the first quartile, and third quartile of the distribution and the internal horizontal line is the median. Whiskers extend from the box out to the most extreme data value within 1.5 by the interquartile range. The boxes have lines at the lower quartile, median, and upper quartile values. The whiskers are lines extending from each end of the boxes to show the extent of the range of the data. The outliers are displayed by a cross. Outliers, displayed by a cross, are data with values beyond the ends of the whiskers. Italic values indicate the number of localscale correlations significant at twosided 95% confidence level according to a random phase test[START_REF] Janicot | Sahel drought and ENSO dynamics[END_REF].

Acknowledgements: We acknowledge the FRIENDAOC group and Senegal DNM for providing us the rainfall data. R. Marteau is partly supported by the AMMA program. Based on a French initiative, AMMA was built by an international scientific group and is currently

funded by a large number of agencies, especially from France, UK, US and Africa. It has been the beneficiary of a large financial contribution from the European Community's sixth Framework Research Program. Detailed information on scientific coordination and funding is available on the AMMA International web site: http://www.ammainternational.org. ECMWF ERA40 data used in this study have been freely obtained from the ECMWF Data Server (http://www.ecmwf.int). We thank Gil Mahé and Benjamin Sultan for fruitful discussions.

Lastly, we thank two anonymous reviewers and the editor of this paper (D. Straus) for their constructive comments which help us on clarifying the goals and results of our paper, and lastly Bradfield Lyon (IRI, Columbia University) for his careful reading of the revised version of this paper timeseries of onset date (bars), seasonal amount (circle) and frequency of occurrence of rainfall (upper triangle).


Franz Chouly

Annemie Van Hirtum

Xavier Pelorson

Yohan Payan

Van Hirtum

Obstructive sleep

Keywords:

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Obstructive sleep apnea (OSA) is defined as the intermittent cessation of breathing during sleep, caused by airway obstruction [START_REF] Young | The occurrence of sleep-disordered breathing among middle-aged adults[END_REF]. To study this phenomenon, a physical model of the airflow inside a constriction is described in [START_REF] Hirtum | In-vitro study of the fluidstructure interaction during obstructive sleep apnea. 28 th Congrès de Biomecanique[END_REF], associated to experimental data from an in-vitro set-up. This paper introduces a numerical model of the fluid-walls interaction in the pharynx and then compares simulations with experimental data.

Material and Methods

In ( 2) is presented an experimental setup, that tries to reproduce the morphology of the upper airways. The « tongue » is a cylinder inserted into « the pharynx », a square rigid pipe. The cylinder can either be rigid or deformable, with latex full of water. On figure 1, the finite element model of the latex cylinder is plotted at its rest position in black. It reproduces latex mechanical properties (Young modulus = 1.5 MPa, Poisson's ration = 0.49). An internal pressure of 400 Pa over atmosphere is applied (water pressure). The geometry of the model and the boundary conditions have also been chosen as close as possible as those of the setup. The pressure due to the airflow is computed using the Bernouilli law and an assumption on the location of the flow separation point (3). Resulting force on surface of each element is obtained by integration of pressure. Because of small deformation hypothesis, a linear relation between constraints and deformations can be computed using a finite element solver (Ansys). Model deformation induces a new geometry, thus a new pressure distribution from which comes a new deformation. The algorithm stops when equilibrium is obtained (quasi-static hypothesis).

Results

First simulations are provided with a pressure drop of 800 Pa. The model is thus deformed due to the application of a negative pressure in the constriction area (Venturi effect) and a resulting decrease of the constriction height is observed (fig. 1,grey). This behaviour is in agreement with in-vitro experiments. Moreover, volume flow velocity limitation is observed (fig. 2), which is coherent with in-vivo measurement provided during hypopnea (4).

Discussion and Conclusion

Using a simple but physically founded numerical model of the interaction between airflow and pharyngeal walls, encouraging preliminary results were obtained. The next step will be to quantitatively compare the model predictions with in-vitro measurements. The model will be improved, first, to get a behaviour as realistic as possible, next, to be in agreement with anatomical and physiological considerations. These conditions are fundamental if we want to use the model for sleep apnea syndrome prediction.

Fig. 1 :

 1 Fig. 1 : The model in rest position (black), and deformed after an inlet pressure of 800 Pa (grey). 64 finite elements are used for the cylinder wall.

Fig. 2 :

 2 Fig. 2 : Curves volume flow rate / inlet pressure, for the deformable model (solid line), and a rigid model (dashed line).