Johara Berriane
email: johara.berriane@gmail.com

Sub-Saharan Students in Morocco: Determinants, Everyday Life, and Future Plans of a High-Skilled Migrant Group

Keywords: African migration, high-skilled migrants, migration transitions, Morocco, student mobility

Based on a study of sub-Saharan students in Morocco, this paper addresses the relationship between international student mobility and high-skilled migration and analyses how the increasing movement of sub-Saharan students to Morocco contributes to Morocco's transition to being a country of immigration and to its integration into the sub-Saharan migratory system.

By studying the migration trajectories of sub-Saharan students, the article shows how three factors influence the students' movement to Morocco: their aspirations to expatriate, their growing up in cultures of migration and the existence of social networks linking the students to Morocco. The experience of otherness in a transit and immigration country such as Morocco contributes further to the shaping of an identity as transmigrants among students who consider their stay in Morocco as a first step on a longer-term migration that might lead to a second emigration or a permanent settlement in Morocco.

Introduction

Since Mohammed VI became king in 1999, the Moroccan state has made significant efforts to become more involved on the African continent. The kingdom has been carrying out a more active co-operation policy with its sub-Saharan neighbours, reviving and strengthening the bilateral cooperation programmes developed since Moroccan independence in 1956. Following complications in the Western Sahara decolonisation process and the OAU (now the African Union) having recognised the Sahrawi Arab Democratic Republic, Morocco withdrew from the African organization in 1984 [START_REF] Barre | Les relations entre le Maroc et les pays d'Afrique subsaharienne[END_REF]). The new African policy aims to counteract Morocco's isolation from the African Union,to gain more support for its sovereignty claims over the Western Sahara province and to defend Moroccan commercial and economic interests in Africa [START_REF] Wippel | Le renouveau des relations marocaines avec l'Afrique subsaharienne: la formation d'un espace économique transsaharien?[END_REF]). The country is more particularly involved in several sub-regional organisations such as the Community of Sahel-Saharan States (CEN-SAD) since 2001 or ECOWAS since 2005, to compensate for its isolation from the pan-African organisation.

Furthermore, the kingdom has participated in the construction of a road that links Senegal with Morocco [START_REF] Wippel | Le renouveau des relations marocaines avec l'Afrique subsaharienne: la formation d'un espace économique transsaharien?[END_REF], thus helping to increase the circulation of goods and people between West Africa and Morocco. Since the early 2000s, Moroccan companies have also been increasingly investing in African markets. The Moroccan banking sector in particular (Brack 2014: 93), as well as several Moroccan new communication and information technologies (NCIT) companies and consulting groups are nowadays present in West African countries.

Morocco's regional integration within West Africa is represented in official national discourse as the result of historical and cultural relations that have linked Morocco with countries to the south for centuries; relations in which Moroccan kings are portrayed as having played a crucial role, especially as religious leaders [START_REF] Sambe | Islam et diplomatie: la politique africaine du Maroc[END_REF].

While Morocco is attempting to reconnect with West Africa politically and economically, a reintegration from below seems to be taking place simultaneously through the increase in sub-Saharan migration flows, contributing to considerable changes in Morocco's migration patterns. In fact, since the late 1990s, trans-Saharan movements have been characterised by transit migration, and trade routes formerly taken by caravans have been used by lorries transporting migrants (Bredeloup and Pliez 2005: 6-7). Although these migrants aimed to reach Europe, they would stop in North African countries, including Morocco, sometimes for a considerable period of time. The kingdom's new awareness of its African identity can therefore also be seen as a result of its role as transit and destination area for sub-Saharan migrants.

Together with Morocco's economic development, the reinforcement of European border controls in 1999 (Natter 2013: 18) has transformed Morocco into an attractive destination for migrants (Bensaad 2005: 28). Although the number of sub-Saharan individuals living in Morocco is estimated to be comparatively small, the migration issue has recently entered the Moroccan public sphere. This led to a more visible political engagement with sub-Saharan migrants [START_REF] Pian | Entre 'visibilisation' et 'invisibilisation', les migrations subsahariennes au Maroc[END_REF] and to the regularisation of undocumented migrants in 2014. While sub-Saharan 'transit' migration in Morocco has been the subject of numerous studies (e.g. [START_REF] Alioua | La migration transnationale des Africains subsahariens au Maghreb: l'exemple de l'étape marocaine[END_REF][START_REF] Escoffier | Transmigration et communautés d'itinérances au Maghreb[END_REF][START_REF] Khachani | Le Maroc comme espace de transit[END_REF], older migration flows and circulations, which are also increasing, have remained understudied. This is the case, for instance, of sub-Saharan students whose number has recently increased in Morocco.

Morocco has, in fact, become a preferred country for sub-Saharan students to receive their training. Since the 1970s, the training of white-collar workers of sub-Saharan origin has formed an integral part of Moroccan-African bilateral cooperation [START_REF] Barre | indépendance: actes de la journée d'étude organisée par l'Institut des études africaines et le département de droit public de la faculté des sciences juridiques[END_REF] and has been constantly developing over recent years. In addition to the official channels allowing and subsidising young sub-Saharans to come and study in Morocco, the country is also welcoming more and more students who are heading for private education establishments. This paper analyses sub-Saharan student movement to Morocco and its relation with broader immigration trends and Morocco's recent foreign policy towards Africa. The aim of this study is to show to what extent students' move abroad and stay in Morocco may develop into, or form an integral part from the very beginning of, a long-term migratory plan and how this contributes to their identity formation as migrants.

The article is based on material collected at two different periods of time. The first set of data was collected in 2006, during a three-month research project conducted in Rabat, and is based on a quantitative survey and semi-structured interviews. 150 sub-Saharan students were interviewed during the quantitative survey. Among them, 79.4% were from West African countries and 76.6% from francophone countries; 23% of the students were women, 79.4% were between 20 and 25 years old and 94% had been living in Morocco for less than five years.

Due to access problems, only three students from private schools could be included in the survey. On the basis of the results from this first survey, one-to two-hour interviews were conducted with 16 randomly selected students. The main themes of the interview looked at their travel and life experiences in Morocco, their relationship with their home country and their future projects. Three interviewees were from Senegal, four from Mali, one from Niger, two from Comoros, one from Burundi, one from Cameroon, one from Burkina Faso, one from Cape Verde, and one from the Congo (DRC). Among this group, five students were women.

In summer 2012, a short quantitative investigation was conducted in order to complete and update the 2006 data, analysing the migratory trajectories of 95 out of the 150 students interviewed six years before.

After presenting some theoretical reflections on the link between student mobility and migration, the second part of this article will describe the characteristics of sub-Saharan student movement to Morocco. In the third section, the determinants of this student mobility are analysed. The fourth part concentrates on the Moroccan experience and its repercussions on the students' self-perceptions. Finally, the last part focuses on those aspects of student life, which could be seen as resembling migrant or even transmigrant life.

Student Mobility and High-Skilled Migration

A recent, but growing literature on the relationship between student mobility and economic migration has highlighted the similarities between students and high-skilled workers, since students represent 'a potential human capital asset for sending countries' (Freitas et al. 2012: 2). This is reinforced by the fact that international students are likely to stay in their training country for work after completing their studies. Studying abroad is often conceived as a strategy to enter a foreign labour market and hence to realise a migration aspiration (Coulon and Paivadi 2003: 45;[START_REF] Rosenzweig | Consequences of Migration for Developing Countries[END_REF]. However, some people also choose to study for a specific degree abroad based on the needs of their home country, as a strategy to return home and find a job (Levatino 2014: 8).

The theoretical debates on the effects of student mobility (and high-skilled migration in general) on the country of origin have developed two different scenarios. On the one hand, the concept of 'brain drain' became prominent within 'dependency thinking' and the historicalstructural Marxist paradigm of the 1970s (Freitas et al. 2012: 3). It emphasises the negative effects of scientific migrations on origin countries, because they tend to empty developing countries of their scientific resources. Often, brain drain is accompanied by the phenomenon of brain waste, in which qualified migrants, once they arrive in the destination country, end up taking jobs that are below their skill level [START_REF] Hunger | Brain Gain': Theoretical Considerations and Empirical Data on a New Research Perspective in Development and Migration Theory[END_REF]).

On the other hand, new approaches to international migration that became more influential in the 1990s have been focusing on the migration processes themselves rather than limiting the analysis of migration to push and pull factors. Indeed, migration studies have incorporated the fact that migration is seldom limited to a single, one-off move from one country to another.

Instead, migrants often circulate between the home and host country or countries, a phenomenon which has accelerated over the past decades partly because of cheaper means of transport [START_REF] Ma Mung | La circulation migratoire. Bilan des travaux[END_REF][START_REF] Tarrius | Territoires circulatoires des migrants et espaces européens[END_REF]. The size of migratory social networks, i.e. the interpersonal links that connect migrants who are already settled with new migrants and nonmigrants living in the home country, also contributes to this process [START_REF] Boyd | Family and Personal Networks in International Migration: Recent Developments and New Agendas[END_REF][START_REF] Massey | Theory of International Migration: A Review of Appraisal[END_REF]. By keeping up these links and maintaining relations with geographically remote communities, migrants are increasingly assuming the character of transmigrants, i.e. migrants who 'develop and maintain multiple relations -familial, economic, social, organizational, religious, and political -that span borders' [START_REF] Glick-Schiller | Transnationalism: A New Analytic Framework for Understanding Migration[END_REF]. Recent migration studies therefore no longer analyse migrants' individual and collective identities within a localised geographical context, because they can have transnational cultural references from various origins and go back and forth between different areas.

The circular and transnational dimension of migration has also become visible among highskilled migrations, as the establishment of transnational scientific communities reduces the classic dichotomy between the home and host countries [START_REF] Dia | Déterminants, enjeux et perceptions des migrations scientifiques internationales africaines: le cas du Sénégal[END_REF]. In this context, the concepts of brain gain and brain exchange have emerged, to stress the positive effects of scientific migrations that contribute to the circulation of knowledge and the formation of scientific networks between scientific diasporas and their home countries, rather than emptying origin countries (Meyer 2012: 67). Thus, even students who decide to enter the labour market of their training countries might play a crucial role in the development of the academic field of their home countries.

These theoretical reflections mainly draw on studies that investigate student movement to highincome countries, i.e. traditional immigration countries. How do these theoretical insights play out in developing countries, such as Morocco, that have sent and are still sending students and highly-qualified migrants abroad [START_REF] Bouoiyour | Brain Drain or Brain Gain? The Case of Moroccan Students in France[END_REF]) and that have high unemployment rates among their university graduates? Does Morocco represent a potential labour market for sub-Saharan students? And to what extent does Morocco's current situation as a transit and immigration country for sub-Saharan migrants affect the life experiences and future projects of foreign students?

Characteristics of sub-Saharan student migration in Morocco

obtained a grant from the Moroccan state and who study in public universities, and students who do not receive such a grant and who usually attend private establishments. Although the former type of student migration has been going on longer than the latter, both flows have increased during the last decade, a trend that illustrates the interrelations between Morocco's regional integration in sub-Saharan Africa and the increase in overall sub-Saharan mobility.

Grant-holding students

In recent years, the number of sub-Saharan students registered with state-run establishments has been growing steadily. The training of white-collar workers by Morocco dates back to the early 1970s, but it was limited to a small number of students from Morocco's favoured partner countries such as Senegal, Guinea or Gabon. Over the last decade in particular, the numbers have grown considerably. While during the 1994-1995 academic year just 1,040 sub-Saharan students were registered with Moroccan state-run establishments, ten years later there were 4,477 (Direction de l'évaluation et de la prospective 2005), and in 2013-2014, their number reached 5,160 -out of a total number of 8,859 foreign students in Morocco (http://www.enssup.gov.ma).

Most sub-Saharan students come from the eight French-speaking countries of West Africa (53% of sub-Saharan students and 32% of foreign students in Morocco). Senegalese students made up the largest proportion (506). However, a growing number (13%) of students also come from Portuguese-, Spanish-and English-speaking countries such as Guinea Bissau, Ghana or Equatorial Guinea. Most students are men: in 2008-2009, only 26% of the sub-Saharan residents studying in public universities in Morocco were women (http: //www.enssup.gov.ma).

The most sought-after courses are economics and law (39%), technology (23%), natural science (18%) and medicine (15%) (Direction de l'évaluation et de la prospective 2005). Given that the majority of these disciplines are taught in French, sub-Saharan students in Morocco only rarely speak Arabic. During the pre-colonial period, Morocco played an important role in the regional transfer of knowledge across neighbouring regions through religious education (Fall 2004: 280) Given that education in Morocco is largely financed by the Moroccan state, the training of sub-Saharan grant-holders is organised and managed by the Ministry of Foreign Affairs. The number of registrations and grants is set on a country-by-country basis, and depends on the diplomatic ties that exist with the country of origin. Most of the students who are registered with state-run establishments are grant-holders. The grant includes free training in a public university or vocational training institution and a stipend of 750 dirhams per month. Although the country of origin is responsible for the selection of the students and selection criteria vary, a good score in the baccalaureate examination is most often a determining factor. Half of the students I interviewed had spent part of their school career in a private school and thus came from a fairly privileged background. However, students from lower social strata do also have access to these grants. Through this active education policy aimed at stimulating student migration from sub-Saharan African, the Moroccan state complements and reinforces its political and economic interests in the region.

Students in private schools

In addition to student migration to state-run establishments, sub-Saharan students increasingly enroll in privately-run establishments in Morocco. This mobility is much harder to study since there are no official data about it, but there is evidence that the number of foreign students registered with private establishments has increased considerably. In 1998-1999, 1,120 foreigners were registered in private schools, in 2010-2011 there were 4,000, representing 10% of all students registered at privately-run establishments in Morocco (Laouali and Meyer 2012: 116).

A few Moroccan private schools such as ISIAM, Hightech or Sup'management have particularly focused on students from sub-Saharan francophone countries, sometimes offering merit-based scholarships and having representation offices in West African capitals (Berriane 2012: 161). Other schools recruit sub-Saharan students in order to advertise and attract more students from the region (Touré 2014: 34). Given that fees in Moroccan private schools or universities range between 2,200 and 5,500 euros per year (Touré 2014: 33), students generally come from privileged family backgrounds.

However, there are many similarities and interrelations between both forms of student mobility.

In fact, it is very common for sub-Saharan students to switch from one type of institution to another. In the Comoros Islands, for example, Morocco is a favourite country in which to study, and students who do not get the chance to sign up straight away for state-run universities head off to private schools. Once in Morocco, they do however try to get into state universities (Interview 8). Thus student mobility is not just related to the opportunity provided by a study grant and free education. While state-sponsored study channels are used as a means to come and study in Morocco, they also indirectly stimulate student migration to the private academic sector.

The determinants of sub-Saharan student mobility: cultures of migration and transnational social networks

The decision to leave

Sub-Saharan students' main motive for coming to Morocco is to improve their future life prospects. Also, studying in Morocco proves to be a good -and sometimes the onlyopportunity to leave one's country, to study, and thus improve one's living standards (Interview 10). Indeed, students often stressed the lack of alternatives and the fact that the destination does not always play a key role in their migration decisions. As a student from Niger explained, 'For me there was no choice. I got my baccalaureate, and this was the first grant that came my way, so I took it' (Interview 6). Many students would have preferred to study in Europe, but given the lack of opportunities they have settled for coming to Morocco (Interview 7). Morocco is also easier to access for the nationals of several countries such as Congo, Ivory Coast, Guinea, Mali, Niger or Senegal since they do not need a visa to enter the country. Furthermore, many sub-Saharan students who decide to come to Morocco are motivated by the idea of having a mission to accomplish for their country. Being selected to come to Morocco is seen by some as an obligation to go and receive education elsewhere to help build up their country (Interview 6; Interview 3). Moreover, parents often play a major role in the decisionmaking process. Often, they are the ones who encourage or even oblige their children to leave the country and prepare the migration for them, as a Comorian female student told me: 'Well, it's my parents, right, they told me to do it and I said yes' (Interview 9).

Finally, travel and escape are often mentioned by sub-Saharan students as important motives for their migration. A stay in Morocco is seen as a way of leaving, of discovering another world, of living out an adventure. This is particularly evident in the story told by a Congolese student who comes from a family that is scattered across a number of European and African countries.

She wanted to study in a country that no one in her family had yet visited, and the possibility of getting a grant for Morocco seemed to be a good opportunity (Interview 2). The existing literature on high-risk sub-Saharan migrations, such as irregular migration through the Sahara Desert or the Mediterranean Sea, acknowledges that seeking adventure is part and parcel of many migrants' motivation to migrate (Bredeloup and Pliez 2005: 14-15). The insights of my study suggest that this is also true for student migration.

Migration decisions are always influenced by a multiplicity of motives and the quantitative study for this paper has confirmed this in the context of student mobility. While 36% of the students interviewed stated that it was the grant that motivated their decision to come to Morocco, the country's political stability, the experience of being abroad and the brighter prospects for future studies were also put forward. For students originating from non-Frenchspeaking West African countries, learning French also played a major role in the choice of the country.

Socio-cultural backgrounds: migrant societies?

At a time when migration opportunities are gradually becoming scarce and any means of getting out of one's country are good enough, student migration turns out to be a good opportunity to emigrate, even if it 'only' leads to Morocco. Omar, a Senegalese student in journalism, pointed at the prestigious character of migration within his origin country: 'Well in Senegal, if I've got two sons or three sons abroad, that's good, even if you're studying or working; the thing is to have family abroad, they like it, they like that [in Senegal]' (Interview 7).

Furthermore, the survey has shown that students usually come from families and social backgrounds where migration is highly valued and an established way of life. Indeed, 59.3% of my interviewees have family members living abroad and 51% of these members are brothers or sisters. Students usually belong to families that are scattered across different African and European countries, with a particularly large group in France (see Table 1).

[insert Table 1 here]

Students with family members abroad were particularly influenced by the picture of foreign countries painted by relatives visiting home: There's family who have already gone, so you see, you get ideas about the family, when you're little and your big brother is in France, he sends stuff, he sends mobile phones home, you see it and you say, oh, that's what France is about, I've got to do anything to get away, that's your dream and you work like stink to make it come true (Interview 7).

Student migration seems to be a direct or indirect strategy to live a migrant life, whilst also having the privilege of advanced university education. In addition to the official channels which encourage this migration, there are social networks that influence the choice of Morocco as a destination and which demonstrate that Morocco's connection with the sub-Saharan migratory system started long before the so-called 'transit' migration of the 1990s and 2000s.

Links with Morocco

For many students (43%), links with Morocco already existed at the time of their departure, mainly through relatives or acquaintances who live or have lived in Morocco for professional reasons, or to study. Indeed, 30% of students interviewed have a family member who has already studied in Morocco (Survey 2006).

Sometimes, key figures in the country of origin can act as role models. In the Comoros Islands or Gabon for instance, 'big names' and 'well-known people', including ministers, have studied in Morocco, attracting young school leavers to follow their example (Interview 9). Thus, Moroccan university education has gained a good reputation in many sub-Saharan countries and former students from Morocco can easily enter the labour market of their home countries (Bredeloup 2009: 274-75). The news about those returning and their success at home or elsewhere stimulates further student migration to Morocco. Thus, social networks -through personal ties or/and information channels -exist behind this student migration and play a role in sustaining student flows towards Morocco. Despite this partial familiarity of Morocco as a country, the actual migration is experienced as a break in the students' lives, given that their stay abroad is frequently accompanied by significant obstacles and difficulties that challenge the image that people in their home community have of Morocco.

The stay in Morocco: rupture and the experience of otherness

The students' accounts in 2006 reveal that the journey to Morocco represents a break in their lives, as they are facing a country that has only recently started to receive larger numbers of sub-Saharan migrants and that stigmatises them and pushes them away -in stark contrast to what they were expecting. Very often, the experience of otherness during their stay has a profound effect on their worldview and students withdraw into sub-Saharan spaces in Morocco to define new forms of identity and belonging.

The journey: a rite of passage?

Accounts of students' arrival and their first impressions of Morocco are highly representative of the importance they attribute to the journey itself. It was astonishing to see that all students, without exception, could remember the exact day they arrived in Morocco, even though for some a considerable amount of time had passed since then. The journey itself holds a crucial place in their memories and was seen as an adventure, for most of them the very first journey abroad in their lives, associated with separation from their families and parents, whom most of them have not seen since that time, and with the abrupt entry into adult life (Interview 3). More than anything else, leaving their families and living autonomously in Morocco is experienced as a test of their courage and maturity (Interview 10).

Grant holders undertook the journey in a group. Once at the airport, they met the other students with whom they were to share this experience. They were often accompanied by an embassy official -sometimes they even flew on the presidential aircraft which had been put at their disposal for the day (Interview 6). This did not only trigger a sense of pride and privilege to be chosen to study for the country, but also created a feeling of being part of an official delegation (Interview 15). Upon their arrival in Morocco, the reception process was overseen by the student offices of the respective countries, with support from the embassy.

After this initial phase spent with their fellow countrymen, they went their separate ways across the country. At that moment, many of these young people, who tend to come from relatively protected social environments, for the first time faced problems which they had never previously encountered, such as official procedures and financial problems (Interview 3). Some realised their grant would barely cover their needs (Interview 6). Others discovered it was difficult to rent private flats in a country where the norm was for young people only to leave the parental home once they were setting up their own family, and that it was not considered appropriate for groups of young single people to rent a place together (Interview 5).

Shattered points of reference: Morocco and the relationship with religion

Despite the existence of information channels and sometimes even considerable communication with acquaintances in Morocco, knowledge about Morocco before migration seems to be very minimal. However, one dominant idea about Morocco that students have before arriving is the kingdom's association with Islam. For all students, Morocco was seen as a very Islamic country, in which the whole of society was organised by religion: 'A Muslim country [where] the girls would be wearing veils, with clothes right down to their feet' (Interview 12). This idea was equally present among Muslims and Christians and offers a perfect example of the effects of Morocco's political strategy in Africa, in which religious diplomacy and especially the Moroccan king's religious authority are utilised in order to gain more allies on the African continent [START_REF] Sambe | Islam et diplomatie: la politique africaine du Maroc[END_REF]. The association between Morocco and Islam also shapes student migration, especially by women. In fact, women interviewed in 2006 arrived in Morocco with the expectation that they were going to wear a veil. Furthermore -although only 23% of sub-Saharan students are female -interviews show that Morocco is seen, particularly among those coming from Muslim communities, as a possible destination for girls. This is based on the idea that young female students would find themselves in a safe environment in Morocco, encouraging their families to choose this destination for them (Interview 8; Interview 13).

Once in Morocco, however, students encounter a society that is much less religious than expected, especially in large Moroccan cities such as Rabat. For some, this contrast between what was expected and what was actually found in Morocco had repercussions on their own attitudes toward religion. Omar sums up his astonishment at the attitude displayed by his university colleagues: I noticed it the first day, it really astonished me. Before I came, I thought Morocco was Islam, and all that; everyone goes off to pray when they should, and all that; and I noticed as soon as I came here, in class when the Muezzin gives the call to prayer, and all that, I'd go off to pray and others just stayed there, chatting away, chatting away, I was saying it's time to pray, and all that, they were messing around, pretending not to hear, I go to pray, I always go to the same place, and they don't pray. That astonished me, I wasn't expecting that, especially because you hear people say that Morocco, the Maghreb, they're Arabs, it's closer to Islam than we are (Interview 7).

The lack of religious practice among Moroccans surprises, given that they -belonging to a country that presents itself internationally as a model for Islam -should be acting as role models. Indeed, in its foreign policy towards West Africa, Morocco has been emphasising its role in the spread of Islam and the religious authority of the king as 'commander of the faithful' is also recognised by some West African religious groups [START_REF] Sambe | Islam et diplomatie: la politique africaine du Maroc[END_REF]. In response to the lack of religious practice among Moroccans, Coming from a Sufi family, Omar, for instance, has withdrawn into his own community and joined a small association created by Senegalese students belonging to this same brotherhood on the university campus. Being Muslim does not therefore necessarily result in better integration into Moroccan society.

In other life accounts, living in Morocco has led to a complete re-evaluation of attitudes towards religion. For Othman, another Senegalese student who had been counting on his stay in Morocco to strengthen his faith, his worldview was shaken:

When I came, people said, oh there you won't have any trouble, they'll even be telling you to continue praying because you're going to a Muslim country; it'll strengthen your faith. When I got here, I was a bit surprised on the first Friday, I went past a Mosque and I saw boys and girls arm-in-arm, walking past the Mosque; I'd thought it would be like Saudi Arabia (Interview 4).

Since coming to Morocco, Othman has completely stopped practising his religion. Whilst some are shocked by Moroccan society and withdraw into the heart of a religious community which they rebuild for themselves, others start to question their personal relationship with religion once in Morocco.

Whilst Moroccans' religious practice is covered at length in the accounts given by Muslim students, Christians usually engage with the country's Christian communities immediately after their arrival (Interview 12; Interview 3). In the city of Rabat, the Catholic and Protestant churches have been reactivated since 1980, notably due to the influx of Christian sub-Saharan students. Among the staff of both churches, a large number originates nowadays from sub-Saharan countries. These institutions represent spaces where Christian students spend a short time immersed in an atmosphere that, they say, reminds them of their home community (Interview 15; Interview 1).

The withdrawal into 'sub-Saharan' religious spaces is, however, also a reaction to the stigmatisation that students experience by Moroccans and that also contributes to the shaping of sub-Saharan identities.

Stigmatisation and 'black' identity: meeting places

From the students' accounts it is possible to identify three places in which students encounter Moroccan society: the street, the neighbourhood and the university. Each of these places is associated with different perceptions and experiences of their interactions with Moroccans.

All students had negative experiences in the street, which they see as a reaction to their phenotype. Students say they are insulted in the streets, are called 'azzi' -a name with negative connotations used to describe people of dark skin colour -and sometimes stones are thrown at them. In short, harassment can be a daily occurrence. In working-class districts in particular, children laugh and chant this name. It is not the children's laughter that shocks them most, but rather the failure of parents and other adults to do something about this behaviour (Interview 3).

In addition to being seen as they often find themselves treated like illegal immigrants. For Fatou, this has become part of daily life, and she often hears herself being called 'harraga' in the street, a name given to migrants emigrating illegally to Europe. Fatou is studying in Oujda, a city in the north of Morocco, not far from the Spanish enclave of Melilla (Interview 13). In this city and its surrounding area, there is a sizeable community of sub-Saharan migrants attempting to enter Spain. Therefore, sub-Saharan students in Oujda have been particularly subject to stigmatisation. Being mistaken for irregular migrants, some of them have even been expelled to the Algerian border during police raids (Berriane 2012: 166).

However, the lumping together of sub-Saharans and (irregular) 'transit' migrants is not limited to the north of the country. Idrissa, who lives in Rabat, tells how he was mistaken one day for an illegal migrant begging for alms: 'I asked a guy the way to, I don't know, a restaurant or something, I was with friends. I said please sir; he didn't even let me finish; I said please sir; he told me "I don't have money"' (Interview 10). Thus, in the anonymous setting of the street, students are confronted with frustrating situations and become conscious of their differences.

For students who live in flats, their neighbourhood (mostly working-class districts) represents another side of Morocco. Interviews revealed that these neighbourhoods often remind students of their country of origin. They tend to enjoy warm friendships with neighbouring families, who welcome them and adopt them into their own families (Interview1; Interview 13). A student in Salé explained how neighbours who spoke little French would try to speak to him regularly in the street in order to practise their French (Interview 11).

The third -and maybe most important -space of encounter between students and the host society is the university. In the accounts given, the scepticism and mistrust between sub-Saharan students and their Moroccan classmates and professors is noticeable. Once more, students see a link between their different phenotype and Moroccans' efforts to distance themselves. This is Christine's explanation for why her Moroccan classmates approached her, who was light-skinned, in particular: They tried to approach me simply because I had a different skin colour from my compatriots. They couldn't understand it, they said how come you're like that and your compatriots are black, and I said yes, but there are also mixed-race people in my country (Interview 2).

Christine's account also illustrates the reciprocity of this distancing and how it is reflected in the spatial organization of classes: I had compatriots in the same class who, hum, let's say, were black, who had already formed a clan; and when I got there I saw the blacks; well, I thought, I could go with the blacks, but that wasn't very good; I don't like this clan business; so with that I thought no, I'm going to try to integrate; so I just decided to sit anywhere in the class and that's how I came to speak to my neighbour in class who became my first friend; her name is Mounia (Interview 2)

The reciprocal segregation between Moroccan and sub-Saharan students is, however, in part a communication problem. In fact, sub-Saharan students are often more at ease speaking French, while Moroccan students prefer to speak Arabic among themselves. According to sub-Saharan students, the 'ignorance' of their Moroccan classmates also explains their behaviour towards sub-Saharan students. By the simple act of coming to Morocco, sub-Saharan students have had an experience of travel to a foreign country, which their Moroccan classmates were mainly lacking.

The spatial segregation is further linked to the stigmatisation of sub-Saharan students by their professors: 'There's a sentence that shocks every sub-Saharan student who arrives. It's when a Moroccan intellectual says to them: "you Africans"' (Interview 1). These representations are perceived as a humiliation by sub-Saharan students since their professor's image of Africa is mainly influenced by negative stereotypes linking 'Africa' to the desert, poverty or war (Interview 14). With time, they learn to deal with this situation by stressing their level of knowledge, distancing themselves from their Moroccan classmates and professors. Compared with Moroccans, they feel open and cosmopolitan, if not 'citizens of the world' (Interview 1).

Encounters with Moroccan students and people in the streets lead to the development of a collective consciousness, or even a common identity in response to similar experiences. Given that the hostile, at times racist, behaviour of many Moroccans is associated with their dark skin, this same aspect becomes an identifying factor among sub-Saharan students. Indeed, in their accounts, sub-Saharan students would describe themselves most of the time as 'black', also to differentiate themselves from their Moroccan environment. Thus, the phenotype, origin of their stigmatisation, becomes the reference point of their self-identification.

It is interesting to see that they describe themselves as 'blacks' and not as 'noirs' [the French word for black]. This might be linked to the fact that the word 'black' has also entered the French language and can be found in discussions on multicultural France as having a 'Black, Blanc, Beur' ('Black, White, Arab') culture. The term 'black' might therefore reflect the desire to belong to a black community that goes beyond the borders of the African continent. In contrast with the Moroccan society, which they experience as western and Europeanised, they construct an African identity. Moroccan society is experienced as being cold, closed in upon itself and sterile, characterised by individualism, a lack of solidarity. By contrast, 'black' society is characterised by solidarity and hospitality, with tradition and religion playing a key role.

You see here, I have to say, Moroccans tend to be more European, because when you see the families, there's one family over here, another one over there, and they don't pull together like at home, see! […] here, the people are always shut away, if rights (Alioua 2009: 279-303;Feliu i Martínez 2009: 343-362), a shift has been observed in students' discourses. Thus, in 2012, a Senegalese journalist who had studied in Morocco described the racist and discriminatory behaviour of his Moroccan fellow students and former professors in a special issue published in a Moroccan journal [START_REF] Bâ | Dans la peau d'un Noir au Maroc[END_REF]. Today, sub-Saharan student associations in Morocco have also become more vocal about the stigmatisation sub-Saharans are facing. However, while sub-Saharan students feel concerned about the situation of their 'irregular' countrymen, they also distance themselves radically from them, although they often share similar aspirations to emigrate. Meeting other Africans plays a key role in the students' self-identification. Within the cosmopolitan African community, however, different sub-communities and identities are established, with language and nationality being the most important reference points. It is for instance customary to talk of French speakers, English speakers or Portuguese speakers, who see themselves as distinct groups, and to attribute particular character traits to the other groups.

Between community life

Most French speakers, for example, describe Portuguese speakers as being more 'Latinos' than 'African', because of their creole culture and strong links to Portugal (Interview 4).

But, given the existence of supporting structures set up by the national student offices, the most prominent aspect for identification is nationality. The integration of new arrivals into the community of their compatriots is so effective that national consciousness can arise or develop during the stay in Morocco. Thus, one Fulbe student from the Casamance region of Senegal (which has a longstanding separatist movement) actively developed a stronger 'Senegalese' identity by spending time with other Senegalese students and learning to speak Wolof once in Morocco (Interview 4).

Community life in Morocco: caught between solidarity and control

The national communities, when they are of a considerable size, therefore play a major role in students' lives. The community is experienced as a source of support and solidarity. However, it is also seen as an organ of social control. Students feel compelled to observe the rules and customs of the home country, and female students in particular feel they are being monitored and restrained in their freedom to act. In fact, the lifestyle lived by female students in Morocco can have repercussions on their reputation upon returning to their home country. A Comorian student, for example, had serious problems with her family when she took the liberty of plaiting her hair in Morocco since, according to Comorian etiquette, such a hairstyle is only worn by girls of dubious reputation (Interview 8). This is an illustration of the informative and supportive but also controlling role played by transnational networks between Morocco, the home country, and other migrant communities.

These communities are too small and understudied to assess their influence within the larger transnational community. However, the way in which the Moroccan experience is lived out and the different possibilities for self-identification mirror to some extent the lives of transmigrants.

Sub-Saharan students may for example feel black in one particular setting, Burkinabe in another, and elsewhere go on to identify themselves with the cosmopolitan Christian community. Whilst they remain in a fairly small community, their stay in Morocco is an exemplary transnational experience which, given the students' aspirations, could be continued in other countries.

Altered plans for the future

The students' migratory plans were only rarely restricted to their studies in Morocco. In fact, 82% of the students interviewed in 2006 said that they wanted to continue their studies in another country, or even work there. The most desirable destination among French speakers, Portuguese speakers and English speakers alike was France, mentioned by 55.9% of the students. This destination makes sense in educational terms, given that studies in Morocco take place within an educational system based on the French model and may therefore represent a first step towards studies abroad. France is followed by Canada (15.3%), the USA (9%), the United Kingdom (7.2%), Belgium (6.3%) and Portugal (1.8%). Italy, the Netherlands, Tunisia, Japan and Malaysia were each mentioned only once (Survey 2006) .

Whilst they hoped that they would be able to continue along this path and reach new destinations, students were also aware of the limits of their ability to migrate. Thus, a number of them expected to stay in Morocco for a few years or more, whilst developing professional links with their country of origin. Othman explained: I'd prefer to do it here even if it's just two years' experience before moving on, just think, if I spend two years working for the Moroccan press. I'm working like a diplomat behind the scenes, because I still think I'm well placed to build understanding between the two countries. (Interview 4)

The stay of former sub-Saharan graduates in Morocco can stimulate links and professional contacts between the country of origin and Morocco, or even enable the circulation of knowledge and know-how.

The survey conducted six years later (in 2012) shows that the plans to reach new destinations were rarely fulfilled. Among 95 of the students I had interviewed in 2006, 67 had graduated and 28 were still studying. Among the 67 graduates, 26 had gone back home, 25 were still in Morocco and five were working in a developed country (Survey 2012). Although the numbers provided by this survey are not representative, they show some interesting trends. While the majority of former sub-Saharan students aspired to a second migration, only a few were able to realise this wish. In contrast, Morocco seems to become a country of settlement and work for sub-Saharans who graduate there.

Due to capitalist restructuring, social changes and the demographic transition that Morocco is facing today, the country is entering a migratory transition phase characterised by the increase in both emigration flows and movement back and forth, and the number of immigrants from sub-Saharan Africa who will settle permanently in Morocco (de Haas 2014). While sub-Saharans settling in Morocco are usually portrayed as unskilled labour migrants, the student mobility studied in this article seems to indicate that the circulation of high-skilled individuals between sub-Saharan Africa and Morocco is also increasing. Some sectors, such as the French-language press sector or telecommunication engineer companies, already employ a large number of former sub-Saharan students who have stayed in Morocco. For Moroccan companies that are investing in Africa, sub-Saharan graduates from Morocco may also represent an important resource as middlemen between their Moroccan employer and their country of origin. However, sub-Saharan graduates are mainly hired as trainees and rarely receive permanent work contracts (Berriane 2012: 171), since foreigners only receive a work permit for jobs for which Moroccans do not have the needed professional qualifications [START_REF] Khrouz | Politiques' publiques et présence des étrangers au Maroc[END_REF].

The survey also identified many students who, having finished higher education courses, now work in international call centres which have been outsourced to Morocco. But, apart from Senegalese nationals, who are allowed to work legally without a work permit, sub-Saharans working in call centres are often there on an illegal basis and thus can easily be exploited by their employers. In order to avoid illegality and to keep their residency status, many former sub-Saharan students who are working in call centres register at private schools, without however attending the courses. Thus, despite the high unemployment rate, especially among university graduates, some work sectors in Morocco provide students with an alternative to returning to their home country and allow them to build up their own professional existence in Morocco. However, the difficulty for foreigners in Morocco to obtain work permits contributes to rather temporary settlements and precarious life situations.

Conclusion

Based on the study of sub-Saharan student mobility in Morocco, this paper addresses the relationship between international student mobility and high-skilled migration. It has been shown that the sub-Saharan student's decision to move to Morocco is based on aspirations similar to those of other migrants. The prestigious character of education abroad, the fact that students grow up in cultures of migration and aspire to emigrate are all factors influencing the student's move abroad. Further, the choice of Morocco as training country is not only due to the bilateral agreements between Morocco and sub-Saharan states but is also influenced by the existence of social networks linking the students to the host country. In addition, the experience of otherness in Morocco contributes to shaping a sense of belonging among students and their identification with a larger transnational and cosmopolitan community of sub-Saharan Africans.

Like other sub-Saharan migrants temporarily settling in Morocco, students see the country as ideally one stage of a longer migration -one that is supposed to be followed by further migration for study or work. However, like other migrants transiting through Morocco, students rarely achieve a second move to a developed country, and staying in Morocco becomes an alternative to returning to their home country. Former sub-Saharan students tend therefore to stay in Morocco, even though the difficulty in getting work permits and the high unemployment rate among university graduates in Morocco leads to temporary and precarious work conditions.

However, Morocco's increasing economic integration in the sub-Saharan region and the establishment of Moroccan companies in Africa might contribute in the near future to an increase in demand for high-skilled labour that has been socialised in both sub-Saharan countries and Morocco. This might contribute to a better professional integration of sub-Saharan high-skilled migrants in the Moroccan labour market and might further influence Morocco's transition from an emigration to an immigration country, reinforcing even more the transnational movements back and forth between Morocco and sub-Saharan Africa.

Tables with captions

  . Today, Islamic studies are taken by only 2% of all sub-Saharan students enrolled in Moroccan public universities. Yet, Morocco does still provide religious training, both for Muslims and for Christians. In 2012, an ecumenical institute was founded in Rabat by the Catholic and the Evangelical church (L'Opinion 2013) and a new institute for Islamic theology was founded in Rabat in March 2015 to train sub-Saharan students as imams and preachers (http: //habous.gov.ma).

  you turn up you have to ring the doorbell before you can go in. It's not like that at home. […] It's like everyone's keeping the others at arm's length, it's really not what you expect […] Because that's more like it is in European life, because like in Europe people don't know one another, you say hello [and] everyone gets on with their own stuff. (Interview 10) It was also striking to see how Morocco's new role as an immigration country has changed students' attitude towards Moroccans. In 2006, my informants rarely described the behaviour of people in the streets as racist. Although students distanced themselves from Moroccans and tended to describe them as ignorant, they rarely openly criticised their behaviour. With the new public awareness of Morocco's role as a country hosting immigrants and the growing political mobilisation of African migrants and local civil society asking for more protection of migrants'

  and the desire to escape: the creation of 'transmigrants'6.1. Multiple African identitiesWhilst identifying themselves as a group distinct from Moroccan society, sub-Saharan students also have other points of reference. Particularly those living in Rabat in the international student halls of residence spend most of their time in a cosmopolitan African setting, an 'Africa in miniature' (Interview 3). This discourse, which promotes the idea of intercultural exchange, is fostered by the workings of the diplomatic process. Since 1981, the Confederation of Foreign African Pupils, Students and Trainees (CESAM) in Morocco has been representing the students within the country and working in collaboration with the Moroccan International Cooperation Agency (AMCI), the institution responsible for organising the education of African students. The chief role of this confederation is to support students, to organise activities throughout the year, and to represent African countries in Morocco.

Table 1 :

 1 Countries of residence of family members living abroad(Survey 2006)

	Country	Number	Percentage
	France United States	42 s 13	28.0 8.7
	Portugal	9	6.0
	United Kingdom	4	2.7
	Nigeria	3	2.0
	Other European countries 7	4.6
	Other African countries	7	4.6
	Other countries	4	2.7
	No family abroad	61	40.7
	Total	150	100.0

Acknowledgements

I thank Katharina Natter for her instructive feedback and help during the preparation of the manuscript.

Funding

This work was supported by the German Academic Exchange Service (DAAD); the International Migration Institute; and the Chaire d'Études Africaines Comparées at the University Mohammed VI, Rabat.

Appendix

[insert Table 2


Nathalie Jarosz

Benjamin Loubet

Laurent Huber

MODELLING AIRBORNE CONCENTRATION AND DEPOSITION RATE OF MAIZE POLLEN

Keywords: atmospheric dispersion, Lagrangian model, turbulence, particles, Zea mays. 1

The introduction of genetically modified (GM) crops has reinforced the need to quantify gene flow from crop to crop. This requires predictive tools which take into account meteorological conditions, canopy structure as well as pollen aerodynamic characteristics. A Lagrangian Stochastic (LS) model, called SMOP-2D (Stochastic Mechanistic mOdel for Pollen dispersion and deposition in 2 Dimensions), is presented. It simulates wind dispersion of pollen by calculating individual pollen trajectories from their emission to their deposition. SMOP-2D was validated using two field experiments where airborne concentration and deposition rate of pollen were measured within and downwind from different sized maize (Zea mays) plots together with micrometeorological measurements. SMOP-2D correctly simulated the shapes of the concentration profiles but generally underestimated the depositions rates in the first 10 m downwind from the source. Potential explanations of this discrepancy are discussed. Incorrect parameterisation of turbulence in the transition from the crop to the surrounding is probably the most likely reason. This demonstrates that LS models for particle transfer need to be coupled with air-flow models under complex terrain conditions.

INTRODUCTION

Pollen dispersion has been the subject of an increasing number of studies since the introduction of genetically modified (GM) crops because of the need to maintain seed purity. In Europe, the main objective for maize (Zea mays) crops has been to quantify gene flow from transgenic to non-transgenic crops as there is no risk of hybridisation with its wild relative, teosinte [START_REF] White | Of genes and genomes and the origin of maize[END_REF][START_REF] Matsuoka | A single domestication for maize shown by multilocus microsatellite genotyping[END_REF] because it does not grow there. However, teosinte does grow in Central America and the risk of hybridisation has become a subject of scientific inquiry [START_REF] Doebley | Molecular evidence for gene flow among Zea species. Genes transformed into maize through genetic engineering could be transferred to its wild relatives, the Teosintes[END_REF][START_REF] Baltazar | Crop-to-crop gene flow: dispersal of trangenes in maize, during field tests and commercialization[END_REF].

Many models of pollen dispersion have been based on observed levels of outcrossing on target plants in the vicinity of an emitting source plot [START_REF] Lavigne | A pollen dispersal experiment with transgenic oilseed rape. Estimation of the average pollen dispersal of an individual plant within a field[END_REF][START_REF] Klein | Estimation de la fonction de dispersion du pollen. Application à la dissémination de trangènes dans l'environnement[END_REF]. Such studies can give direct estimates of outcrossing rates, but are of limited use as predictive tools because they are only valid for the meteorological conditions found during the experiments. A few models of atmospheric pollen dispersion based on concentration and deposition measurement exist [START_REF] Mccartney | Wind dispersal of pollen from crops of oilseed rape (Brassica napus L.)[END_REF][START_REF] Jackson | Pollen dispersal models in Quaternary plant ecology: Assumptions, parameters, and prescriptions[END_REF], but to our knowledge, none has been applied to maize. In this study, we evaluate an alternative and complementary approach using a Lagrangian Stochastic (LS) model to simulate wind dispersion of maize pollen. The model, called SMOP-2D (Stochastic Mechanistic mOdel for Pollen dispersion and deposition in 2 Dimensions) predicts pollen concentration and deposition rate downwind from an emitting field. SMOP-2D is a mechanistic model that considers atmospheric turbulence, pollen aerodynamic characteristics and canopy structure. It also includes an empirical parameterisation of the turbulence field for heterogeneous landscapes. These features allow the investigation of contrasting scenarios. LS models have proved to be accurate for calculating the dispersion of atmospheric gases [START_REF] Wilson | Review of lagrangian stochastic models for trajectories in the turbulent atmosphere[END_REF]. They have been successfully extended to simulate heavy particle dispersion [START_REF] Walklate | A markov-chain particle dispersion model based on air flow data : extension to large water droplets[END_REF][START_REF] Reynolds | A lagrangian stochastic model for heavy particle deposition[END_REF][START_REF] Wilson | Trajectory models for heavy particles in atmospheric turbulence : comparison with observations[END_REF] and have been used to estimate fungal spore release rates [START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF]).

Here we validate the LS model SMOP-2D by comparing calculated concentrations and deposition rates with those measured during field experiments conducted in 2000 [START_REF] Jarosz | Field measurements of airborne concentration and deposition of maize pollen[END_REF] and 2001 [START_REF] Jarosz | Etude de la dispersion atmosphérique du pollen de maïs. Contribution à la maîtrise des risques de pollinisation croisée[END_REF].

MATERIAL AND METHODS

Model

SMOP-2D is a Lagrangian stochastic (LS) model in 2 dimensions (horizontal downwind (x) and vertical (z))

that simulates the wind dispersion of pollen grains by calculating a large number of individual trajectories.

SMOP-2D is a version of the LS model initially developed for atmospheric ammonia dispersion that was adapted for pollen dispersion [START_REF] Loubet | Modélisation du dépôt sec d'ammoniac atmosphérique à proximité des sources[END_REF][START_REF] Jarosz | Field measurements of airborne concentration and deposition of maize pollen[END_REF], and is very similar to the spore dispersal model reported by [START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF]. Pollen can be treated as a passive scalar, with a settling velocity V s added to the vertical velocity component, provided that the size is in the range 20 µm ≤ diameter ≤ 300 µm [START_REF] Wilson | Trajectory models for heavy particles in atmospheric turbulence : comparison with observations[END_REF]. The displacement of individual pollen grains is calculated using the following two-dimensional joint stochastic differential equations: [START_REF] Rodean | Stochastic Lagrangian Models of turbulent Diffusion[END_REF][START_REF] Thomson | Criteria for the selection of stochastic models of particle trajectories in turbulent flows[END_REF][START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF]. In this study, these coefficients are those detailed by [START_REF] Wilson | Trajectory curvature as a selection criterion for valid lagrangian stochastic dispersion models[END_REF] for models preserving the mean direction of the fluctuating velocity vector, which corresponds to the Thomson's model (1987). They are therefore not given here. Due to gravitational forces and inertia, heavy particles do not follow the fluid trajectories exactly [START_REF] Sawford | Lagrangian statistical simulation of the turbulent motion of heavy particles[END_REF]. This effect is taken into account by reducing the fluid velocity time scale along a particle trajectory, τ p , compared to that for a fluid trajectory, T L [START_REF] Sawford | Lagrangian statistical simulation of the turbulent motion of heavy particles[END_REF]:

d u = a u dt + b u dξ u dx = udt dw = a w dt + b w dξ w dz = (w-V s )dt (
τ p = T L 1+ ⎝ ⎛ ⎠ ⎞ β V s σ w 2 ( 2 )
where β is an empirical dimensionless constant. In this study β was taken to be 3 [START_REF] Snyder | Some measurements of particle velocity autocorrelation functions in a turbulent flow[END_REF]. But, the value of β for particle dispersion is still subject to debate (see e.g. [START_REF] Wilson | Trajectory models for heavy particles in atmospheric turbulence : comparison with observations[END_REF].

Turbulence field

The parameterisation of the turbulence for horizontally homogeneous conditions is described in [START_REF] Loubet | Modélisation du dépôt sec d'ammoniac atmosphérique à proximité des sources[END_REF], and includes vertical profiles of U, W, σ 2 u , σ 2 w , u'w' and T L . A simple empirical parameterisation of the turbulent field in the transition zone between two different canopies was chosen. The transition zone was defined as the location between the upwind position, x upwind , where the turbulent field is defined by the characteristics of the upwind canopy, and the downwind position, x downwind , where the field is defined by the downwind canopy (Figure 1). At any position, x, within this zone, each vertical profile of a given turbulent characteristic was interpolated between the upwind and downwind equilibrium profiles using a 3 rd degree polynomial P. To simplify the expression of the polynomial, a normalised distance X was used:

X = x -x upwind x downwind -x upwind ( 3 )
The polynomial was defined as P(X) = -2 X 3 + 3 X 2 . This ensured the continuity of the profiles and their derivatives over the transition zone: it satisfied four constraints: P(0) = 0, P(1) = 1 and P'(0) = P'(1) = 0. Mass conservation was ensured by calculating W as the integral over z of the derivative of U over x (-dU / dx). This parameterisation allows the most influencing parameters to vary realistically over the transition zone. However, the parameterisation of u'w' profiles may not be ideal, as these profiles should increase at the transition and decrease afterwards [START_REF] Bradley | A micrometeorological study of velocity profiles and surface drag in the region modified by a change in surface roughness[END_REF], whereas here the profiles change smoothly from upwind to downwind. The parameterisation of the flow in the transition zone was designed to get a realistic but simple turbulence field. It was therefore not considered necessary to add more complexity to the stochastic model. Hence we did not include the horizontal derivatives in the coefficients a u , b u , a w and b w as should be done under non-homogeneous turbulence [START_REF] Leuzzi | Particle trajectory simulation of dispersion around a building[END_REF]. However, the effect of including these derivatives was evaluated: it generated unsteadiness in the trajectories, but did not show great differences in concentration and deposition rates, when compared with the effect of a modification in the turbulence field. (insert Figure 1 about here)

Model parameters and input variables

SMOP-2D considers canopy and pollen characteristics, and micrometeorological variables (Table 1). The canopy parameters for each field are: the downwind fetch (x c ); the height (h c ), the roughness length (z 0 ); the displacement height (d); and the leaf area density (LAD), made up of the horizontal and vertical projections (LAD x and LAD z ). Pollen aerodynamic characteristics were accounted for using a Gaussian distribution of the settling velocity V s . Unless otherwise stated, a mean of 0.31 m s -1 and a standard deviation of 0.08 m s -1 were taken for the distribution of V s , which is consistent with [START_REF] Di-Giovanni | The variability in settling velocities of some pollen and spores[END_REF], although smaller means have been measured by others [START_REF] Aylor | Settling speed of corn (Zea mays) pollen[END_REF][START_REF] Jarosz | Etude de la dispersion atmosphérique du pollen de maïs. Contribution à la maîtrise des risques de pollinisation croisée[END_REF]. The simulations were carried out over a horizontal distance, x D , and vertical height, z D . The area was divided into a grid with N x horizontal and N z vertical elements for concentration estimates. The grid in the maize canopy had more tightly spaced vertical layers (N h ). (insert Table 1 about here)

Concentration and deposition

The model outputs were pollen concentration (C); deposition rate to the ground (D g ); and deposition rate to vegetation surfaces (D v ). The concentration C was calculated for any point (i, j) of the grid (i = 1 to N x and j = 1 to N z ) as [START_REF] Flesch | The footprint for flux measurements, from backward lagrangian stochastic models[END_REF]:

C(i, j) = V source × 1 N p ∑ n = 1 N p T n (i, j) / V(i, j) ( 4 )
where V source is the volume of the source, N p the is number of trajectories, and T n is the residence time of particle n in the grid division of volume V(i, j).

Deposition within the canopy was expressed as the sum of the contribution due to gravitational settling and the contribution due to inertial impaction [START_REF] Legg | Spore dispersal in a barley crop : a mathematical model[END_REF]. The probability that pollen deposits on the vegetation (D v ) or on the ground (D g ) over a time step dt was calculated according to [START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF].

The deposition rate either at the ground or on the vegetation in the horizontal grid location i (i = 1 to N x ) was specified as:

D g,v (i) = V source × 1 N p ∑ n = 1 N p D n g,v (i) / A(i) (5)
where D n g,v is the probability that the pollen grain n deposits on the ground or vegetation and A is the area available for deposition at distance i.

Model validation

Experimental data

The model outputs were compared with measurements recorded during two field experiments one at Montargis and the other at Grignon, France, in 2000[START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF], respectively (Jarosz et al., 2003;[START_REF] Jarosz | Etude de la dispersion atmosphérique du pollen de maïs. Contribution à la maîtrise des risques de pollinisation croisée[END_REF].

Vertical profiles of pollen concentration were measured at x = 3 m and 10 m downwind from a 20 × 20 m maize plot at Montargis and two 24 × 42 m maize plots at Grignon. Pollen deposition rates were measured between x = 1 m and 32 m in Montargis and x = 1 m and 200 m in Grignon. Micrometeorological measurements were made during the entire pollination period. The plots were isolated from other possible sources of maize pollen: at Montargis, the plot was surrounded by bare soil, and at Grignon, by stubble. The two plots in Grignon were not sown at the same time, so pollen measurements were made at two different flowering dates. Runs were carried out on 12 occasions in Montargis (R1 to R12), and 9 (S 1 9 to S 1 17) and 15 (S 2 18 to S 2 32) occasions in Grignon for the first and second dates, respectively.

General framework

The simulated total area was divided in three canopy zones: one located upwind from the maize crop (zone 1), the maize plot (zone 2); and one located downwind from the maize crop (zone 3) (Figure 1). The maize plot was the only source of pollen. In all simulations, zones 1 and 3 had the canopy characteristics of either bare soil or stubble depending on the chosen experiment location. Only ground deposition was taken into consideration in zones 1 and 3, as the canopies in these zones were short and not dense.

Turbulence

Each field was characterised by: vegetation height, h c i (index i denotes the canopy zone); displacement height d i ; its roughness length z 0 i ; and leaf area density vertical profile LAD i . For the maize plots (zone 2), z 0 and d, were taken as z 0 = 0.1 × h c and d i = 0.7 × h c [START_REF] Kaimal | Atmospheric boundary layer flows, Their structure and measurement[END_REF]. For zones 1 and 3, z 0 i was estimated by fitting measured and calculated wind profiles as explained below (Table2). The mean wind speed U ref at the reference height (z ref ) was estimated from measured friction velocity u * and Monin-Obukhov length L over the downwind field (zone 3), using Monin-Obukhov similarity theory:

U(z) = u * k ⎩ ⎨ ⎧ ⎭ ⎬ ⎫ ln ⎝ ⎛ ⎠ ⎞ z -d z 0 -Ψ m ⎝ ⎛ ⎠ ⎞ z -d L + Ψ m (z 0 / L) (6)
where k is the von Kármán constant and ψ m is the stability correction function given by [START_REF] Dyer | A review of flux-profile relationships[END_REF]:

ψ m ((z-d) /L) = ⎩ ⎪ ⎨ ⎪ ⎧ ln ⎣ ⎡ ⎦ ⎤ ⎝ ⎛ ⎠ ⎞ 1 + x 2 2 ⎝ ⎛ ⎠ ⎞ 1+x 2 2 -2 atan x + π 2 -2 ≤ (z-d) /L ≤ 0 -5.2 ((z-d) /L) 0 ≤ (z-d) /L ≤ 1 (7) with x ((z-d) /L) = (1 -16 ((z-d) /L)) 1/4
. The stability parameter (z-d) /L is negative when the air stratification is unstable and positive when stable.

Within each canopy, the wind speed profile was defined by 1972). The attenuation factor, γ, for open canopies (= 2.5) was used [START_REF] Raupach | Coherent eddies and turbulence in vegetation canopies : the mixing-layer analogy[END_REF]. Measured values of σ w / u * , above the canopy, for all experiments were between 1.3 -1.4, but σ u / u * values changed with the atmospheric stability and wind direction. However, for all simulations, values of σ u / u * = 3.1 and σ w / u * = 1.4

U(z) / U(h c ) = exp [ γ (z / h c -1) ](Cionco,
were used above the canopy under neutral conditions. Stability effects was taken into account as indicated in [START_REF] Loubet | Modélisation du dépôt sec d'ammoniac atmosphérique à proximité des sources[END_REF]. These somehow ideal values were preferred to test the model as measured values may not always be available from field experiments. Values of u * and L -1 were measured for each simulation (Table 2).

Over the transition zone, the x upwind and x downwind distances were adjusted to fit measured wind speed profiles at x = 3 m and 10 m, respectively. They ranged from 3 to 10 × h c , and from 10 to 20 × h c at the upwind and downwind edge of the source field respectively. (insert Table 2 about here)

Canopy structure

The maize leaf area density LAD(z) profile and its projections along the horizontal and vertical plane (LAD x and LAD z ) was assumed to have the same shape for Grignon and Montargis. It was based on measurement of the canopy structure in three dimensions made during the Grignon experiment using a digitiser (Figure 2). A characteristic leaf size (leaf width) was used to estimate pollen deposition on vegetation. To minimise the number of parameters the leaf width was fixed at 0.05 m for maize and 0.01 for bare soil or stubble. The height and size of the tassels (the "source" of pollen) were measured during each experiment and are given in Table 1.

(insert Figure 2 about here)

Numerical settings and validation strategy

The number of trajectories, N p , for each simulation was 100000. The size of the total area was z D = 10 m, and

x D = 130 m and 254 m for Montargis and Grignon, respectively. The number of grid divisions was N x = 100 for the horizontal, N z = 20 for the vertical and N h = 10 within the canopy.

During the experiments, the pollen release rate to the atmosphere was not quantified (see [START_REF] Jarosz | Field measurements of airborne concentration and deposition of maize pollen[END_REF]. However, this variable constitutes a major input of SMOP-2D and needs to be determined. Therefore, the source strength for each simulation was estimated by "inversion" of the model. Similarly to the approach of [START_REF] Aylor | Estimating spore release rates using a lagrangian stochastic simulation model[END_REF], the inversion was carried out by first running the model with a release rate of 1 grain m -2 s -1 and calculating the concentration profile at 3m. Measured concentrations were plotted against calculated concentrations and a linear regression with zero intercept was performed. The slope of this regression was taken as the estimation of the actual source strength.

Since the source strength of the model was chosen to make measured and modelled concentrations fit at x = 3 m, the quality of the model was validated using measured and calculated deposition rates and vertical concentration profiles at x = 10 m.

RESULTS

Simulations were done on 8 runs in Montargis, 5 for S 1 and 14 for S 2 in Grignon. Figure 3 shows vertical profiles of measured and simulated concentration at x = 3 m and 10 m and measured and simulated deposition rates downwind from the source plot, for four representative runs (R6, R7, S 1 13 and S 2 21). As the parameters z 0 , d, x downwind and x upwind were determined for each run by fitting the measured and simulated vertical profiles of horizontal wind speed at x = 3 m and at x = 10 m, these profiles are also shown in the figure for the same runs.

Concentrations at Grignon were measured to a higher level (at z = 6.4 m) and deposition rates were measured further down (x = 200 m) than at Montargis. (insert Figure 3 about here)

Airborne concentration

There was good general agreement between measured and simulated concentration profiles at x = 3 m and x = 10 m: the order of magnitude of the concentration at x = 10 m is correct; and the shape of the concentration profiles at x = 3 and x = 10 m was reasonably reproduced. However, at x = 3 m, the model systematically underestimates the concentrations at heights z = 2 m and 4 m, the modelled pollen plume settling down too quickly compared to field measurements. Figure 4 shows the vertical profiles of the mean relative error between measured and modelled concentration (i.e. the difference between the two concentrations divided by the measured concentration). The agreement between the model and the measurements tended to be better for the

Deposition rates

The model tended to estimate the order of magnitude of deposition rates relatively well (Figure 3b). Figure 5 shows the mean relative error between the simulated and measured deposition rate as a function of the downwind distance to the source. In all cases, deposition rates were underestimated close to the source. For the Montargis runs the deposition rate was always underestimated by approximately 40% for x ≤ 16 m and up to 80% for x = 32m. In contrast to Montargis, for the Grignon runs deposition rates were very well simulated for x = 8 m: relative errors were close to zero. But, they were overestimated at distances of 16, 60 and 120 m and underestimated at x = 200 m (note that only series S 1 gives measurements for x = 200 m). (insert Figure 5 about here)

DISCUSSION

In all the simulations presented in this study, the model tended to underestimate pollen deposition rate in the vicinity of the maize plot whereas it correctly simulated the concentration levels. It could be argued that correctly modelling deposition rate near the source is not essential if the object is to determine potential outcrossing, which takes place at larger distances. However, local deposition is a factor in the quantity of pollen available for long-range transport and is therefore important to determine. Various possible explanations are explored below to explain why the model underestimated deposition rates.

Deposition measurements

Deposition rates may have been influenced by the height at which the measurements were taken (25 and 30 cm high in both sites). To explore this, a simulation was run where all particles were deposited at a height of 30 cm. There were no significant differences between deposition rates at 30 cm and at ground level, suggesting that deposition rates at 0 and 30 cm are identical. This is reasonable since the time spent by the pollen in the layer 0-30 cm is on average equal to 0.3 / V s ~ 1 s, which is small. It was also thought that the shape of the deposition containers may influence pollen deposition by modifying local turbulence. [START_REF] Mccartney | Spore deposition velocities measured over a barley crop[END_REF] have shown that the number of fungal spores collected on horizontal microscope slides openly exposed was almost twice that collected on slides placed on a table or at the bottom of large beakers. Hence, collecting pollen in containers could have led to the underestimation of the deposition rate, although in these experiments the containers were short (less than 7 cm high) compared to those used by [START_REF] Mccartney | Spore deposition velocities measured over a barley crop[END_REF] which were 215 mm high. Thus, sampling errors due to the use of containers would be expected to have led to underestimates and not overestimates of deposition rate. Such errors would have made the comparison with the model worse.

Therefore, effects of pollen collector position and shape are unlikely to explain the discrepancy between measurements and simulations.

Concentration measurements

Another possible explanation for the discrepancy between measurements and model is an underestimation of the concentration by the rotating-arm pollen traps. This would lead to the underestimation of the source strength and in turn to the underestimation of the deposition rate by the model. If this were the case, the correct concentrations would be higher, and so would the source strength and the predicted deposition rates. However, an increased deposition rate at all distances would not lead to a better fit of the measurements as the model underestimates the deposition rates only near the source (Figure 4).

Settling velocity

The underestimation of deposition close to the source could be linked to an erroneous parameterisation of the distribution of settling velocities for maize pollen. In all runs, the distribution of V s was taken from Di-Giovanni et al. (1995), who found a Gaussian distribution with a mean of 0.31 m s -1 and a standard deviation of 0.08 m s -1 .

Observations by one of the authors [START_REF] Jarosz | Etude de la dispersion atmosphérique du pollen de maïs. Contribution à la maîtrise des risques de pollinisation croisée[END_REF], as well as experiments by [START_REF] Aylor | Settling speed of corn (Zea mays) pollen[END_REF], gave a wider range of values for V s , with generally lower means from 0.20 m s -1 to 0.32 m s -1 , with an average of 0.26 m s -1 . However, using a smaller value of V s would increase underestimation of deposition rate by the model. Indeed, it is generally thought that heavier pollen or clusters settle more quickly than single pollen grains. Clusters of maize pollens with 2 or 3 pollen grains have been observed in laboratory experiments by [START_REF] Ferrandino | Settling speed of clusters of spores[END_REF], [START_REF] Di-Giovanni | The variability in settling velocities of some pollen and spores[END_REF][START_REF] Aylor | Settling speed of corn (Zea mays) pollen[END_REF], although such clusters have not been reported in the field. [START_REF] Ferrandino | Settling speed of clusters of spores[END_REF] have reported that maize pollen doublets and triplets settle 40% and 73% faster than single pollen grains, respectively. The model assumed that all pollen grains were singles. To examine the underestimation of settling velocity, the model was run for different sized clusters of pollen grains. The settling velocity of a cluster of N maize pollen grains has been shown to be V s N = V s N [START_REF] Ferrandino | Settling speed of clusters of spores[END_REF], giving V s 2 = 0.37 cm s -1 and V s 3 = 0.45 cm s -1 for doublets and triplets respectively. Figure 6 shows the concentration profiles and the deposition rates simulated for run S 1 13, with V s ranging from that for single pollen to a cluster of 5 grains (which are unlikely to exist). The model simulated deposition rates near the source better for higher V s but did not correctly simulate the concentration profiles, especially at x = 10 m, where measured concentrations were greatly underestimated for high values of V s . The hypothesis of a mixed population of singles and clusters of pollen can be evaluated based upon Figure 6. Since concentration and deposition rate are proportional to the source strength, for a mixed population of pollen, they would simply be a weighed sum of each cluster's concentrations and deposition rates. Therefore, the behaviour of the model remains the same for mixed population as for unmixed ones. These results suggest that it is unlikely that the errors in pollen settling velocity and/or the effects of clusters are solely responsible for the underestimation of deposition by the model near the source. (insert Figure 6 about here)

Pollen resuspension

Pollen resuspended from the ground, or from vegetation, could have contributed to the pollen deposit, hence increasing the measured deposition rates close to the source . [START_REF] Aylor | An aerobiological framework for assessing cross-pollination in maize[END_REF] have shown experimentally that pollen could be quite easily dislodged from maize leaves by either leaf shaking, roll-off or light air flow (0.2 to 0.5 m s -1 ). They have also shown that maize pollen does not stick to leaf hairs. Resuspension has also been observed for other particles in the laboratory [START_REF] Aylor | Rebound of pollen and spores during deposition on cylinders by inertial impaction[END_REF][START_REF] Braaten | Particle resuspension in a turbulent boundary layer-observed and modeled[END_REF][START_REF] Ibrahim | Microparticle detachment from surfaces exposed to turbulent air flow: controlled experiments and modeling[END_REF]. Thus, pollen resuspension from leaves is likely to occur in the field. Simulations (not shown) were performed with pollen sources at two different heights, 1.7 and 2.0 m, corresponding to the height of maximum observed LAD in the crop. Two values of V s were also used: V s = 0.26 m s -1 , which corresponds to fresh pollen and V s = 0.15 m s -1 , which corresponds to dry pollen [START_REF] Jarosz | Etude de la dispersion atmosphérique du pollen de maïs. Contribution à la maîtrise des risques de pollinisation croisée[END_REF]. These sources represented pollen from potential resuspension sites in the maize plot. None of these simulations enhanced the agreement between simulated and measured deposition rates close to the source, suggesting that the discrepancy could not readily be explained by the resuspension of pollen from the crop.

4.5

Effect of the β parameter [START_REF] Wilson | Trajectory models for heavy particles in atmospheric turbulence : comparison with observations[END_REF] reported simulations of the deposition of glass beads (mean diameter ∅ = 107 µm) released from a point source at 15 m high over prairie land. He found that β had a great influence on the deposition rates.

We ran simulations (not shown) with different values of β (β = 1.5, 2, 3, 4 and 5). They showed little influence of β on short-range deposition of pollen. Increasing β seemed to decrease vertical diffusion near the source but also to decrease deposition further downwind.

Turbulence

Another possible cause of the model's underestimation of deposition close to the source lies in the difficulty to correctly describe the turbulent flow in the transition zone at the downwind edge of the source, especially for U, W, σ w and u'w' . For example higher turbulence intensities would induce higher vertical diffusion, which would favour larger deposition rates near the source and increased concentration above the source level.

The topography at Montargis and Grignon was especially complex, and the area downwind from the source could not be considered as a simple rough to smooth transition zone. The maize canopies were only about 20 m long on the downwind side (~ 10 h c ), hence the area downwind from the source was still under the influence of the smooth to rough transition zone of the upwind edge [START_REF] Irvine | The evolution of turbulence across a forest edge[END_REF]. Measurements of turbulence intensities downwind from the plots, using ultrasonic anemometers (Gill, R2 and R3, data not shown), gave an increase in σ w / u * over the standard boundary layer value (~1.7 u * instead of 1.3 u * ) in the first 10 m downwind from the maize plot. Moreover, W measured downwind from the canopy showed a marked downward flow (W ~ -0.7 u * ), whereas the parameterisation used gave W ~ -0.4 u * . These observations are in good agreement with [START_REF] Irvine | The evolution of turbulence across a forest edge[END_REF] for x / h c = 14.5 downwind from a smooth to rough edge, which corresponds to x = 10-15 m in our study. Hence, enhanced σ w and negative W near the source could partly explain higher measured deposition rates, because a negative W directly adds up to the settling velocity, and an enhanced σ w induces a larger diffusive flux (upward but also downward), and hence a larger deposition rate near the source.

Further downwind, the deposition may be reduced by a larger σ w due to the depletion near the source.

Parameterised values of u'w' were much lower in absolute value (by a factor of 2 to 3) than those measured over the canopy and downwind ( u'w' about -4 u * 2 upwind ). [START_REF] Irvine | The evolution of turbulence across a forest edge[END_REF] found an increase of u'w' up to -2.5 u 2 * downwind from a single transition. In the model, higher u'w' , like higher σ w , would tend to both increase upward dispersion and downward diffusion, and therefore deposition. However, the underestimation of u'w' in the model was probably much higher than the underestimation of σ w . Consequently, it is likely that a better parameterisation of u'w' , W and σ w for the transition zone in the model would result in increased agreement between predicted and measured deposition rates near the source.

CONCLUSION

This study shows that SMOP-2D correctly simulated the airborne pollen concentration pattern downwind from a small-sized maize crop but generally underestimated the deposition rates in the first 10 m downwind from the crop. Factors that could account for the discrepancy between modelled and measured deposition rates were evaluated by sensitivity analysis. This analysis led to the conclusion that the underestimated deposition rates were probably not due to: (1) biased concentration or deposition rate measurements, (2) presence of heavier pollen, or clusters of pollens, with higher V s , (3) pollen resuspension from leaves in the plot or the ground, or (4) a wrong value of the β parameter reducing the particle Lagrangian time scale. The analysis suggests that model underestimation of the deposition rate was more likely due to the incorrect parameterisation of the turbulent field over and close to the emitting source. This highlights the need for Lagrangian Stochastic models to be coupled with at least 2 nd order Eulerian flow models if they are to be used for complex terrain.

Many processes apart from pollen dispersal are also involved in outcrossing in maize crops. For example, biological factors such as pollen viability, silk receptivity, synchronisation of timing of flowering between crops, and competition between foreign and local pollen. Outcrossing can also be affected by other meteorological factors, including rain wash out and ultra violet solar radiation (affecting pollen viability). Thus models trying to estimate outcrossing would require either mechanistically or empirically integrating all these features.

Figure captions

Figure 1. Wind speed profiles illustrating the parameterisation of the turbulent exchanges in the transition zone between two adjacent canopies. Interpolation is made between equilibrium profiles in contiguous fields. Here x ci is the downwind fetch of the field i, and x upwind and x downwind are the upwind and downwind distance influenced by the roughness change. V s = 0.26 m s -1 for single grains (black thin line), 0.37 m s -1 for doublets (grey thin line), 0.45 m s -1 for triplets (black dotted line), 0.52 m s -1 for quadruplets (grey dotted line) and 0.58 m s -1 for quintuplets (black dotted dash line).

  1 ) u and w are the horizontal and vertical air velocity components; a u , b u , a w and b w are the Langevin coefficients; and dξ u and dξ w are random numbers drawn from Gaussian distributions with mean zero and variance dt. The Langevin coefficients are functions of the average horizontal (U) and vertical (W) components of air velocity; velocity variances; the shear stress ( u'w' ), and the Lagrangian velocity timescale (T L ). Over a flat homogeneous terrain, W is assumed to be zero. The coefficients a u , b u , a w and b w are determined from the well mixed criterion and the Kolmogorov similarity hypothesis, under stationary and horizontally homogeneous flow

  Grignon runs than those at Montargis. The simulation underestimated the 2 and 4 m concentrations for the 3 m profile by about 50% at Montargis, but by less than 25% at Grignon. The simulation of the 10 m profile at Montargis overestimated concentration by up to 200% (z = 1 and 4 m), while at Grignon errors, for z ≤ 4 m, were usually less than 50%. The better fit at Grignon was probably because the maize plot was larger than in Montargis and completely isolated from other maize pollen sources. (insert Figure4about here)

Figure 2 .

 2 Figure 2. Profile of leaf area densities (LAD) (bold line) used in the model for Grignon and Montargis. The corresponding LAI was roughly 4. The projection of LAD along the horizontal LAD x (grey continuous line) and the vertical planes LAD z (black dotted line) are also represented.

Figure 3 .

 3 Figure 3. Results of Montargis and Grignon simulations (R6, R7, S 1 13, S 2 21). (a) Measured concentration profile (C) at x = 3 m (■) and x = 10 m (□) and simulated profiles at x = 3 m (thin line) and at x = 10 m (dotted line) downwind from the source. (b) Measured (■) and simulated (thin line) deposition downwind from the source (D). (c) Measured profiles of mean wind speed U at x = 3 m (■) and x = 10 m (□) and simulated at x = 3 m (thin line) and at x = 10 m (dotted line) downwind from the source.

Figure 4 .

 4 Figure 4. Mean relative error between measured and modelled concentration in Montargis ( ) and Grignon (S1 ▲, S2 ) at x = 3 m (thin line, full symbols) and at x = 10 m (dotted line, empty symbols) downwind from the source as a function of height z. First, for each simulation, the relative error was calculated as the difference between measured and simulated deposition divided by measured deposition at a given distance. Then, the relative errors were averaged to produce this graph.

Figure 5 .

 5 Figure5. Mean relative error between measured and modelled deposition rates in Montargis (□) and Grignon (S1 ○, S2 △) at different distances downwind from the source. First, for each simulation, the relative error was calculated as the difference between measured and simulated deposition divided by measured deposition at a given distance. Then, the relative errors were averaged to produce this graph.

Figure 6 .

 6 Figure 6. Sensitivity analysis of the settling velocity V s . Concentration profile at (a) x = 3 m and (b) x = 10 m downwind from the source and (c) the deposition as a function of x are represented for simulations S 1 13 with V s = 0.26 m s -1 for single grains (black thin line), 0.37 m s -1 for doublets (grey thin line), 0.45 m s -1 for triplets (black dotted line), 0.52 m s -1 for quadruplets (grey dotted line) and 0.58 m s -1 for quintuplets (black dotted dash line).

  FIGURE 1

Table 1 .

 1 Main input parameters of the SMOP-2D model, with units and typical values used in this study.

	Symbol	Parameter	Units	Typical values
				used in this study
	CANOPY
	x c	Downwind fetch of the field	m	20 -200
	h c z 0 d	Canopy height Roughness length Displacement height	m m	0.1 -0.2 and 2.2 -2.3 0.1 × h c 0.7 × h c
	L f x upwind x downwind LAD (z)	Leaf size Upwind distance influenced by the roughness change Downwind distance influenced by the roughness change m m m Leaf Area Density as a function of z m 2 m -3	0.01 -0.05 3 -10 × h c 10 -20 × h c 0.5 -2.5
	LAD x (z) LAD z (z)	Fraction of the plant projected onto horizontal plan Fraction of the plant projected onto vertical plan	m 2 m -3 m 2 m -3	0 -1.3 0 -0.8
	TOTAL AREA
	0 -x D	Horizontal size of the total area	m	130 or 254
	0 -z D	Vertical size of the total area	m	10
	GRID
	N x	Number of horizontal grid divisions	-	100
	N z	Number of vertical grid divisions	-	20
	N h	Number of vertical layers within the source	-	10
	SOURCE
	N p	Number of pollen grains released	-	100000
	x Smin -x Smax	Horizontal limits of the source	m	0 -20 or 0 -24
	z Smin -z Smax S dens	Vertical limits of the source Release rate of the source	m grains m -2 s -1 1 2.0 -2.3 or 2.2 -2.5
	PARTICLE
	V s std V s β	Mean settling velocity of the pollen Standard deviation of settling velocity Empirical constant in the Lagrangian timescale	m s -1 m s -1 -	0.31 0.08 3
	TURBULENCE
	L	Monin-Obukhov length	m	-2 to -100
	U ref	Mean wind speed at a reference height zref	m s -1	1.72 -10.81
	z ref	The reference height at which wind speed is given	m	50
	C 0 σ u / u * σ w / u * γ	Universal Lagrangian velocity structure constant Ratio of along-wind squared root velocity variance to u * --Ratio of vertical squared root velocity variance to u * -Attenuation coefficient for mean wind speed in the -	3 3.1 1.4 2.5
		canopy
	T L u * / h c	Ratio of the fluid Lagrangian time scale (T L ) times u * to	-	0.3
		hc within the canopy
	Δt / T L	Time step for the particle trajectory as a ratio of T L	-	0.01

Table 2 .

 2 Measured concentrations and deposition rates as well as parameters used in the model for each simulation of Figure3. z 0 is the roughness length, u * is the friction velocity, and L the Monin-Obukhov length over the downwind surface; U(z = 50 m) is the calculated wind speed at z = 50 m over the downwind surface, using the values given in this table for z 0 , u * and L

	Concentrations

* height z (m) for concentration and downwind distance x (m) for deposition rates.

ACKNOWLEDGEMENTS

Many thanks to Jean Louis Drouet for numerically rebuilding the 3D maize structure. We also thank Alastair McCartney for his helpful comments on this paper and Suzette Tanis-Plant for editorial advice. This work was funded by INSU / CNRS, Convention N° 01 CV 081, as well as by INRA (Institut National de la Recherche Agronomique), FNPSMS (Fédération Nationale de la Production des Semences de Maïs et Sorgho) and GNIS (Groupement National Interprofessionel des Semences et plants).