auteur d'un chapitre publié, dans un ouvrage collectif

Research on the family and on households has provoked many theoretical debates, from the functionalist theories of Talcott [START_REF] Parsons | The kinship system of the contemporary United States[END_REF] to the affirmation of Louis [START_REF] Roussel | Evolution récente de la structure des ménages dans quelques pays industriels[END_REF] that there is a plurality of family models, via the William Shorter's demonstration (1977) of the existence of a postmodern family [START_REF] Vimard | Transitions démographique et familiale. Des théories de la modernisation aux modèles de crise[END_REF]).

We will not revisit these debates here. They provide a background, however, for a discussion of the present-day evolution of family and household and their prospects. Although such a discussion has often been based on studies of industrialized countries, it is also relevant for developing countries that are undergoing profound transformations of their kinship structure. 1 It is particularly important for countries of sub-Saharan Africa, where kinship systems shaped the structure of traditional societies.

The following questions must be addressed if we want to make sense of present-day forms of the family and the household: What is the role of kinship relations in the formation of residential units? How permanent are households based on an extended family, and how important is the pattern of nuclearization? Are there types of households, such as single-person or one-parent households, that reflect a certain decay of family structure? Can the presence of a single or dominant model of coresidence be ascertained, or do several models coexist? Are there differentials between sections of the population that can be explained by social class, mode of production, or economic situation?

In order to answer these questions, we have selected Côte d'Ivoire, a country for which we have access to several countrywide sources of data since 1975. These sources have already made it possible to identify certain characteristics and trends of such family structures as the family nucleus and the household. For example, the analysis of the multi-round survey of 1977-78 led to the following main conclusions [START_REF] Vimard | Les noyaux familiaux en Côte d'Ivoire, structures et probabilités de transition[END_REF]:

The nuclear 2 family household presents itself . . . as the dominant form that determines to a large extent the structure of family nuclei and the family life cycle of individuals. It assumes a different weight in various populations, is more widespread in rural than in urban areas, and varies according to demographic characteristics of the head of the unit, being non-existent for women and weak for the youngest and the oldest men. Beside this nuclear unit, widely diffused secondary forms can also be identified, such as the single parent family unit headed by a woman, and non-family units. The importance of links between related or non-related individuals outside of the nuclear component itself should be noted. These family structures that run counter to the exclusive character of the nuclear family are essentially a consequence of the activation of solidarity within extended families, of the development of extra-family structures of co-residence, of female autonomy and of the appearance of new forms of parenthood.

These conclusions were obtained by considering the family nucleus as a statistical unit of observation. They were confirmed by observations of larger units such as households or domestic groups in urban [START_REF] Antoine | Urbanisation et dimension du ménage[END_REF] and rural areas [START_REF] Vimard | Diversité des structures familiales en Côte d'Ivoire, une approche à partir d'études de cas en milieu rural akan[END_REF]. The analysis of household structure in the census of 1988 revealed relatively distinct patterns of household structure by socioeconomic groups, which may thus be characterized as a particular mode of residential aggregation by kinship group [START_REF] Vimard | Conséquences sociales de la structure des ménages selon les groupes socioéconomiques en Côte d'Ivoire[END_REF].

In view of consistent series of observations, it seems useful to seek a more complete view of the evolution of household structure in order to evaluate the persistence over time of these multiple family models as well as their transformations, and to investigate the principles that determine household structure in the communities residing in Côte d'Ivoire. In the following analysis we try to estimate the extent to which, at the global level and for various groups represented in the population, various phenomena have emerged that are manifestations of a relative fraying of the demographic fabric of society: an increase in the number of single-person households, a dominance of the nuclear component of households and even of the mother-child dyad, and the instability of the marital nucleus. These phenomena have become obvious in the last thirty years in industrialized countries, but they can also be observed in the developing world. It is also necessary to document the relevance of developments that are characterized by the survival or reappearance of family solidarities, made concrete by the persistence of the extended household structures that have been observed in African societies [START_REF] Locoh | L'évolution de la famille en Afrique[END_REF][START_REF] Vimard | Modernité et pluralités familiales en Afrique de l'Ouest[END_REF].

The present chapter updates and complements an earlier article [START_REF] Vimard | Évolution de la structure des ménages et différenciation des modèles familiaux en Côte-d'Ivoire 1975-1993[END_REF]. At the time, data were available from the population censuses of 1975 and 1988 and from the 1993 survey of migration and urbanization. Since the 1993 survey was close in time to that of the census of 1988, the analysis was not entirely adequate to evaluate long-term family changes. Today it is possible to use the results of a national survey on household living standards that took place in 1998, while awaiting access to the files of the population census of 1998. The difference between the definition of the household in the censuses and that used at the time of the 1998 survey might have resulted in different classifications of heads and members of households, and therefore in different estimates of the size and composition of households. 3 A comparison of certain general characteristics that are available for the census of 1998 suggests that this did not happen. In 1998, the average size of the household was 5.8 in the census and 5.9 in the living standard survey; the proportions of female heads of households were 16.0 and 15.3 percent respectively; the mean age of household heads was 42.2 and 43.0 years respectively (data from the 1998 General Census of Population and Housing).

Using the 1998 data provides more historical depth, particularly in regard to the changes during the decade of the 1990s, a crucial point if we wish to link the evolution of households with that of the economy and society. The period covered by our sources offers strong contrasts from an economic point of view. The year 1975 is situated toward the end of a stage of intense economic growth, which has been called the "Ivoirian model of development." Per capita gross national product reached its peak in 1980. After that, a severe economic crisis with important social and political consequences resulted in a 30 percent decline of the GNP by 1988, the date of our second observation. The decade 1988-98 was an era of stagnation of production, but particulars varied from sector to sector. Agriculture and the rural areas benefited more than small-scale industrial production and the urban areas from various structural adjustment plans and from the 1994 devaluation of the CFA franc [START_REF] Grimm | De l'évolution de la pauvreté urbaine en Côte d'Ivoire. Une analyse sur 15 ans d'enquêtes ménages[END_REF]. In spite of the crisis, progress as measured by the UNDP human development index continued during the period 1980-98, although at a slower pace than in the preceding decades [START_REF] Talnan | Mutations sociales, crise économique et évolution du modèle de reproduction en Côte d'Ivoire, communication à l'atelier de l'Unité de recherche[END_REF]. This long period of economic upheaval was accompanied by a slowing down of urban growth and a diversification of migration streams. Exhaustion of the soil in the newly exploited parts of the forest regions and an employment crisis in the modern urban sector of the economy resulted in complex patterns of mobility that, more than was the case in the past, combined rural-rural migration, return migration from the city to the countryside, and temporary moves [START_REF] Georges Photios | La Côte d'Ivoire à l'aube du XXI e siècle[END_REF].

Evolution of Household Composition

Three population files were used for this analysis: those of the two first censuses of Côte d 'Ivoire, in 1975 and[START_REF] Locoh | L'évolution de la famille en Afrique[END_REF]

Heads of Household

The sub-population of household heads underwent three evolutions (Table 6.1). First, the share of single-person households decreased after a slight initial increase. Second, there was an important increase in the mean age of household heads between 1975 and 1998, for males as well as for females. And finally, and most importantly, there was a large increase in the proportion of femaleheaded households between 1975 and 1988, followed by stabilization during the most recent period. 5 The share of female-headed households more than doubled in twenty-three years. The increase was proportionately largest among households of more than two members: their number multiplied almost by two and a half. This increase in the proportion of female-headed households between 1975 and 1998 led to a corresponding increase of the population living in such households (Table 6.2). The contribution of women to the family structure increased markedly during the two decades of observation, and in the end was no longer a marginal factor as it had been in 1975.

Changes in the General Composition of Households

During the period of observation, the average size of households increased from 5.5 to 6 persons between 1975 and 1988, and then stabilized between 1988 (6 persons) and 1998 (5.9 persons). (See Table 6.1). 6 This overall increase in size is worth noting, as it occurred during a period marked by a decline of polygyny-the proportion of polygynist among married males drops from 25 to 19 percent between 1975 and 1998-and by growth of the urban population-from 35 to 42 percent of the total population during the same period. These two factors would seem to operate in favor of a reduction in the size of households. Their effect is compensated by various social phenomena that we will examine in the subsequent analysis, and that include a decline in the number of persons living alone and an increase in the number of "other relatives" in the households. The increase in average size was the combined result of changes in the size of households of two persons or more-6.4 in 1975, 6.8 in 1988, and 6.5 in 1998-and of the proportion of one-person households.

Other trends deserve to be noted. The number of non-related individuals per household decreased over the period. However, the size of the family component (head, spouse, children and other relatives) grew from 5.2 in 1975, to 5.5 in 1988, and 5.8 in 1998. This family component increased also as a proportion of all households, from 95 percent in 1975 to 98 percent in 1998. Within it, the various categories of relatives evolved differently; the average number of spouses was stable, while the number of children and other relatives increased (Table 6.1). Thus, the nuclear component increased absolutely from 4.4 to 4.6 persons, but decreased as a proportion of the whole family, from 80 to 78 percent. Households became more family-centered, but not more nuclear, as they included on average more children and more other relatives, but fewer non-related members, in 1998 than in 1975.

These global tendencies seem to confirm certain observations of economists and sociologists on Ivoirian society. They have noted the evolution of kinship solidarity, including the welcoming of the underprivileged in the more well-to-do households at the beginning of a crisis, and the weakening of solidarity as the crisis lasts or intensifies [START_REF] Vidal | Pratiques de crise et conditions sociales à Abidjan[END_REF][START_REF] Jarret | Ajustement structurel en Côte-d'Ivoire[END_REF]. Welcoming the poor may well explain the doubling of the number of the non-related in households between 1975 and 1988, while the strong decline by 1998 would reflect the weakening of social solidarity. Such parallelism over time should be treated with a grain of salt, however. The welcoming curve seems to reach a peak in 1988 if we believe the statistical evidence, whereas the process of expelling guests was already reported earlier in households from Abidjan [START_REF] Vidal | Pratiques de crise et conditions sociales à Abidjan[END_REF]. Similarly, the decline in 1998 occurred at the end of a period during which the general economic situation had been relatively stable.

Changes in the Composition of Households of Two Persons or More

Considering households of two persons or more separately in Table 6.3 controls for the effect of changes in the proportion of single-person households, which will be discussed later. The size of the latter households was relatively stable at the two ends of the period of observation, 1975 and 1998, although it increased in 1988. The trend in the family component is different: it is stable between 1975 and 1998, and grows in 1998. Within the family component, the various categories of relatives change slightly; the decline in the number of spouses and the increase in the number of children and other relatives suggest a tendency toward denuclearization. Most of the variation is in the number of non-related persons, and this accounts for a major part of the change in the average size of households.

Composition of the Household According to Sex of the Head

The growing importance of female-headed households lends special interest to the differences in the make-up of households by sex of their head (Table 6.3). Concentrating again on households with two or more members, female-headed households are in sharp contrast with those headed by men in the following respects:

• they are markedly smaller: 5.0 persons versus 6.7 in 1998; • spouses are almost completely absent, as female heads consist most often of widows or divorced women; • children are fewer, about 2 in contrast with 3 for male-headed households; • other relatives are more numerous: for example, in 1998, 1.7 versus 1.3. 7 On the other hand, the numbers of non-related individuals are comparable. Thus, female-headed households are characterized by a more restricted biological cell, because of the absence of a spouse and a smaller number of children, and by a wider extension in the direction of extra-nuclear kinship. The trends in the average size of these households between 1975 and 1998 runs parallel with that of the male-headed ones: an increase until 1988, followed by a decrease; over the whole period, size increases for both sexes. The evolution by sex leads to the conclusion that the relative stability of the average size of households of more than two persons during our period of observation is principally accounted for by an increase in the proportion of the smaller female-headed households, while the average size increases for both categories of heads of household.

Changes in the Structure of Households by Socioeconomic Groups

General Evolution of Household Structure

A look at the distribution of households by type complements the preceding discussion of size, composition, and sex of head. In the following typology, we distinguish between nine types of households on the basis of the structure of their nuclear component and of the presence or absence of individuals classified as "other relatives." 8 This yields the following types: "living alone," "couple," "single-parent family," "nuclear family," "head of household + other relative," "couple + other relative," "single-parent family + other relative," "nuclear family + other relative," "head of household + non-related" (Table 6.4). 9

For the population as a whole, the dominant impression is one of stability of the various types of households. Some changes in the distribution should be noted, however. First, the proportion of persons living alone declined from 16 to 11 percent of the households. Next, one-parent families increased from 8 percent in 1975 to 13 percent in 1998; the change reflects a decline in marital stability. Finally, the inclusion of "other relatives" in the household showed a slight increase, from 37 percent of the households in 1975 to 41 percent in 1998. This shows the increasing tendency, for at least two decades, to include members of the kinship group of the head of household who are not part of his or her nuclear family.

Household Structure and Socioeconomic Groups

In order to refine our analysis of the typology of households and to investigate the different types of structures by socioeconomic class, we will distinguish between seven socioeconomic groups defined in terms of the type of activity, occupation, and employment status of the head of household: independent farmers, agricultural wage earners or laborers, unskilled workers, clerical workers or managers, artisans or petty traders, employers or professionals, the economically inactive or without a fixed income. 10 These groups have different weights in the population, and these weights change during the period, sometimes significantly. 11 Of particular interest are:

• The attrition of the population engaged in agricultural activities, farmers as well as wage earners and unskilled laborers.

• The decrease in the number of clerical workers and managers, probably as a result of a decade of severe economic difficulties and structural adjustment. In contrast, the share of unskilled workers had regained its 1975 level in 1998, after having been cut in half in 1988, in the middle of the crisis.

• Three groups grew: employers and professionals, the inactive or without a fixed income, and most of all artisans and shopkeepers. The growth of the two latter categories is symptomatic of the changes that took place during the crisis, with the extension of the informal sector, consisting mainly of petty crafts and trade, and the increase in the number of individuals without activity or a fixed income who are no longer welcomed in the less economically destitute households. The growth of the number of employers and professionals suggests that modernization continued during the crisis, and that a modern private sector of small businesses and professionals was expanding.

Ongoing Nuclearization in Most Groups

Socioeconomic groups show clear differences with respect to the structure of their households, and particularly to the process of nuclearization.

It is possible to distinguish between:

• Strongly nuclearized groups. They are those with a majority of households based on a nuclear family, with or without other relatives. In 1998, the following groups were ranked on top: employers and professionals (71 percent); farmers (69 percent); unskilled workers (61 percent); clerical workers and managers (57 percent).

•

Groups with limited nuclearization. Nuclearization concerns less than half the households of agricultural wage earners and laborers (45 percent), inactive persons and persons without a fixed income (44 percent), and artisans or petty traders (39 percent).

Unequal Importance of One-parent Family Households

The proportion of one-parent family households (with or without other relatives), linked as it is with the proportion of female heads of households, is an element that helps distinguish between groups. One-parent families were especially important in 1998 among the inactive or without a fixed income, and above all among artisans and traders, where the change since 1975 is very marked. The growth of the latter category was accompanied by a change in its composition, as more women became heads of household: 15.8 percent of households in 1975 and 31.5 percent in 1998 (Appendix Table 6.A2).

The other occupational categories are less affected by this phenomenon. Note, however, that the increase in the proportion of one-parent family households is general over the period, and is particularly marked among unskilled workers because of the appearance of women in this group. Wage earning confers some autonomy on women.

Differentiation by the Presence of Other Relatives

Socioeconomic groups are also differentiated by the presence of other relatives. Two groups at the top of the socioeconomic scale, employers or professionals, and clerical workers or managers, and one group at the bottom, the inactive or without a fixed income, increasingly included other relatives; more than half of these households contained other relatives by 1998. A third of the other groups included other relatives, and the proportions have tended to decline since 1975, with the exception of agricultural wage earners and laborers, where the proportion was 22 percent in 1998.

Strong Variations in the Proportion of Single-person Households

Households consisting of isolated persons represented 11 percent of the total in 1998, but the proportion varies strongly by socioeconomic category. Such households were particularly important among agricultural wage earners or laborers, and exceeded 10 percent among most categories except employers or professionals (8 percent) and farmers (7 percent). Over the period, the proportions decreased among all groups except farmers.

Diverging Evolution of Family Structure in the Socioeconomic Groups

The various trends that have been described so far show that beyond the global evolution, there were diverging transformations that affected the socioeconomic groups. An overview of these transformations can be obtained by regrouping the seven socioeconomic groups in three larger categories-farmers, "dominated" categories which are characterized by having a vulnerable means of subsistence, and modern categories which enjoy social and economic stability and/or access to a modicum of social and human capital-and by regrouping the types of household into four main categories: isolated persons, one-parent, nuclear, and extended households. 12 The presence of relatives other than the members of the nuclear family can also be examined. Table 6.5 includes only male-headed households, so as to eliminate the effect of different size by sex of the head.

Household Structure and Its Impact on Family and Society

In a community the pattern of household structure is related to family cohesion to the extent that it determines the modalities and the degree of integration of individuals into family units. Thus, the differences in the structure of households by socioeconomic group correspond to differences in the cohesion of family and society. There are four indicators of cohesion: the proportion of persons living alone, the proportion of non-relatives in households, the proportion of relatives in households, and the ratio of the number of children living in single-parent families to the number of children living in nuclear families with both their parents (Table 6.6). The proportion of persons living alone reflects the individualism in a given group, and provides a first index of familial and social cohesion. The proportion averaged 2 percent in 1998, and was very uneven between socioeconomic groups. It declined in all groups over the period, except among farmers, where it was very low from the start in 1975.

The proportion of individuals who are not related to the head of their household is a second indicator, and a more ambiguous one. It reflects lower social cohesion, but also a certain social solidarity with individuals who are not part of the head's kinship group. The proportion underwent a sharp increase in 1988, before reaching its lowest point in 1998. The differences between socioeconomic groups are not very marked, the highest proportions being reached by groups at either end of the socioeconomic ladder while the households of farmers were most often limited to relatives.

The proportion of other relatives in the household reflects the intensity of another ambivalent phenomenon in family life. It corresponds on the one hand to extended family solidarity, mostly toward lateral branches, but also toward grandchildren and parents; on the other hand, it reveals a certain fragmentation of the nuclear family, since most of these other relatives have left their own nuclear family. The share of foreign relatives has clearly increased since 1975 in all groups, but particularly in the households of the inactive or without a fixed income.

The ratio of the number of children in one-parent households to those who live in nuclear-family households reflects the impact of a breakdown of marital cohesion and, to a lesser extent, of extramarital births, on the mode of socialization of children. In 1998, for the whole population, 13.2 percent of the children were raised in one-parent family households. Thus, for every 1,000 children living in a nuclear family, 152 lived with only one of their parents, compared to 135 in 1988 and 91 in 1975. The phenomenon is gaining ground in all groups of the population, except among the inactive or without fixed revenue, where it has always been high but declined between 1988 and 1998. The increase was uneven among the groups, however, and involved more specifically agricultural wage earners and laborers, unskilled workers, and artisans and traders; 34.9 percent of the children in the last category lived in a one-parent family. The degree of marital cohesion influences the mode of socialization of children, which for 90 percent of the children in the other groups occurs in the nuclear family.

If we consider the four indicators together, then agricultural wage earners and laborers, the inactive or without a fixed income, and artisans and traders seem to constitute the groups that are most affected by the decline in familial and social cohesion. These groups also share the most precarious economic conditions, but they are also those where the heads of households, as a consequence of their sex and age, are in a demographic condition that is coterminous with a lack of structure of the family. This is the case for women heads in the group of artisans and traders or in the group of inactive or without a fixed income, as well as for young heads who are wage earners or laborers in agriculture. The demographic characteristics, economic conditions, and family status of these groups are not distinct factors.

On the contrary, familial and social cohesion is found in communities that have an adequate economic foundation, whatever the source of this adequacy-ownership of land or of means of production, a stable wage job, financial comfort, or the like-and one that remains adequate in spite of the uncertainty during crises. This is true for all the better-endowed economic groups

Factors Behind the Complexity of Households

The progress of one-parent families and of the inclusion of other relatives, the stability of nuclearization, and the decrease in the number of one-person households all made Ivoirian households more diverse, more oriented toward the family, and more complex between 1975 and 1998. In other words, households were based on the family more than in the recent past, but the structure of the family took diverse and often complex forms. This complexity varies mainly according to the socioeconomic group of the head of household. What are the characteristics of household heads that are associated with household complexity? Were these factors the same in 1975 and 1998? We try to answer these questions through an analysis of household type by means of a model of ordered multinomial logistic regressions, which seem to be the most appropriate for this type of analysis. 13The Variables Household complexity, the dependent variable, is represented by five types of households, from the least to the most complex, depending on the number of relationships encountered in each type. 14 The categories are as follows: 15 Category 1, no kinship relation: Household head living alone or with non-related persons. Category 2, one kinship relation: Couple; one-parent family; one-parent family + other relatives. Category 3, two kinship relations: Couple + other relatives; one-parent family + other relatives. Category 4, two kinship relations: nuclear family. 16 Category 5, three kinship relations: nuclear family + other relatives.

In the choice of independent variables, our model is constrained by the availability of the same variables at both ends of the period of observation. This compelled us not to retain ethnic group and type of residence, which were absent from one of the files. We also excluded sex from our list of explanatory variables, since female-headed households are, almost by definition, based on a oneparent family. Thus, for this initial analysis, we retained six variables: age, age squared, marital status, socioeconomic group, religion, and years of completed education (table 6.7 and table 6.8). Notes: * When the coefficient > 0, the corresponding explanatory variable indicates that the individual with that characteristics is more likely to choose a complex structure of household. Conversely, when the coefficient is< 0, the corresponding explanatory variable indicates that the individual is more likely to choose a simple structure.

** p = level of significance.

Significance and Impact of the Chosen Variables

In 1975, most of the variables are significant, and the level of significance is low only for age, secondary or higher level of education, and the artisan/trader group. In 1998, these variables have become significant. The former two are positively related to household complexity, the latter one negatively. Farmers, clerical workers or managers, Christians, and without schooling, which were significant in 1975, cease to be so twenty-three years later. The two former ones were favorable to complex households, the two latter ones to simple households. The effect of age and age squared conform to the classical life-cycle pattern of the household. When the household is formed, its head is most often a young adult who lives alone or as member of a couple, and the degree of complexity is low. As age increases, the biological and collateral sphere broadens. At older ages, the structure becomes simpler again, and this results in a negative effect of age squared. Some variables are associated with complexity in 1975 as well as in 1998. These include the variables: married; separated/divorced/widowed, in relation to the increase in household complexity after marriage and after its breaking-off ; and employer/professional, representing the broadening of households in this category that enjoys a certain social and economic well-being. Conversely, other variables are associated with low complexity in 1975 as well as in 1998: age squared (see above); agricultural wage earner/laborer, whose precarious economic conditions limit the opportunity to have a complex household; and Muslim, which cannot be readily explained as the Muslims are often thought to have large households with an extended kinship group. Our model shows that these characteristics of Muslim households are not linked with religion, but with other factors.

On the other hand, it is worth nothing that the variable unskilled worker, which was favorable to household complexity in 1975, had the opposite effect in 1998. The evolution for this group may be due to the effects of the crisis. By making the situation of the wage earner more precarious, it has limited the ability of heads of household to support a large number of dependents. Alternatively, this could be the result of a change in the family model of reference for these heads of household. The changes between 1975 and 1998 could be the result of the crisis, but there is no way to settle the issue one way or the other.

Conclusion

Our analysis of the evolution of household structure from the middle of the 1970s to the end of the 1990s in Côte d'Ivoire, as recorded in three data collection operations, suggests that there is more than one principle of organization of family structure, and that the various socioeconomic groups behave differently. Various forces that bind or dissolve families, such a nuclearization, the hosting of other relatives, individualization or marital instability, are encountered within the households, and account for their particular morphology in line with the distribution of characteristics that vary by socioeconomic group. The particular mix is determined at least in part by the economic and financial ability of the groups to withstand the constraints of the crises encountered by Ivoirian society since the early 1980s, but also in part by the demographic characteristics of sex and age of the heads of household. The structure of households is a joint function of the economic and social position of their heads, but also of the stage of the life cycle in which they are located.

The groups benefiting from the best economic foundations also have the strongest family bonds. Inversely, the groups characterized by precarious economic circumstances, and that have been hit hardest by the crisis, are also most prone to the breakup of the family. For the latter groups, the relaxation of family links is a necessity rather than the choice of a social norm, and it corresponds to a structural collapse due to poverty and crisis. As such, it is very different from what the industrial countries have experienced during the 1970s and 1980s [START_REF] Roussel | Evolution récente de la structure des ménages dans quelques pays industriels[END_REF]).

It appears that the populations of Côte d'Ivoire have conformed to a multiplicity of family models in shaping their dominant household structures. This diversity is not predicated on an opposition between a nuclearization of the family and its extension in the direction of the kinship group beyond the nuclear family unit, as several analyses of family models in the developing world have argued, but rather on the competition between the principles of family cohesion and marital stability on one hand, and between the reality of destructuration, individualization, and marital breakdown on the other. Ivoirian families since 1975 have been characterized as much by the constant or even increasing tendency of certain groups to expand outside of the family nucleus to the larger kinship, as by an increasing frequency of single parenthood, which has been accompanied by a growing role of women in family and society, particularly in the underprivileged section of the population. These general trends, however, must not hide the progress of nuclearization by attrition of the isolated households and rejection of other relatives when a man heads the house.

The acute crisis that affected the 1988 results was accompanied by a marked increase in single parenthood and in the number of non-related persons in households. Ten years later, in 1998, the incidence of single parenthood has remained important, and it appears to have become a long-term structural phenomenon related to a change in the position of women in the economy and society and to a strengthening of their capacity for autonomy in familial and social life. On the other hand, the presence of the non-related has clearly ebbed, indicating that it was a short-term phenomenon linked to the onset of the crisis.

In summary, Côte d'Ivoire in the last twenty years has witnessed an evolution of the family model, that is of the mode of more or less stable communal living specific to economic groups. This evolution is linked to the transformations of marital and kinship solidarity. It developed under the influence of the modernization of socioeconomic structures, which continued through recession and crises. Little by little, the household models diverge by social strata. At the same time, the members of the family nucleus and, beyond them, the members of the kinship group, represent a larger share of households. More than ever, the family is at the heart of the household.

  that of the National Household Living Standards Survey of 1998. Random samples of districts were drawn from the censuses, of 1 in 30 for 1975 and 1 in 35 for 1988. The entire sample of the national living standard survey was used. It had been drawn randomly among 210 clusters drawn from enumeration areas in the census of 1988, weighed to insure the representativity of the sample.

	The household files include: for 1975, 34,842 households comprising a de jure population of
	191,191 persons; for 1988, 44,622 households with a de jure population of 269,623 persons; for
	1998, 4,200 households with a de jure population of 24,560. 4

Table 6

 6

	.1. Change in household characteristics (in percent)
	Characteristic	1975	1988	1998
	Percentage of single person households	16,6	17,9	11,4
	Average age of heads of household :
	Both sexes	37,9	41,0	43,0
	Male	37,9	40,8	42,4
	Female	38,6	42,3	46,2
	Percentage of female-headed households	7,4	15,1	15,3
	Average size (all households)	5,5	6,0	5,9
	Average composition of households
	Spouse	1,0	0,8	0,9
	Children	2,4	2,4	2,7
	Other relatives	0,8	1,3	1,2
	Non related	0,3	0,6	0,1
	Size of the sample:
	Number of people	191 191	269 623	24 594
	Number of households	34 842	44 622	4 200
	Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the
	National Household Living Sandards Survey of 1998.

Table 6

 6

	.2. Changes in the percentage of female heads of household and of the population living
	in their households
		1975	1988	1998
	Female headed single-person households	14,0	19,0	21,1
	Female headed households with 2 persons or more	6,1	14,5	14,6
	Population in female headed households	4,8	11,5	11,4
	Population in female headed households with 2 person or more	4,5	11,3	11,3
	Members of the family component in female headed households with 2 person or more	4,4	11,1	9,3
	Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National
	Household Living Sandards Survey of 1998.

Table 6 .

 6 3. Change in average composition of household, by sex of the head (households of 2 persons or more)

			Spouse	Child	Other relative Non related	Total
	Male	1975	1,3	2,9	1,0	0,3	6,5
		1988	1,1	2,9	1,5	0,7	7,1
		1998	1,1	3,2	1,3	0,1	6,7
	Female	1975	0,1	2,1	1,2	0,3	4,7
		1988	0,1	1,8	1,9	0,6	5,4
		1998	0,0	2,2	1,7	0,1	5,0
	Both sexes	1975	1,2	2,9	1,0	0,3	6,4
		1988	0,9	2,7	1,5	0,7	6,8
		1998	1,0	3,0	1,4	0,1	6,5

Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National Household Living Sandards Survey of 1998.

Table 6 .

 6 4. Type of household by socioeconomic group of the head of household per 100 household in each group (in per cent)

			Head	Couple	One	Nuclear	Head +	Couple	Single	Nuclear	Head +	Percent
			alone		parent	family	other	+ other	parent	family +	non	of
	Socioeconomic group of the head of household				family		relative	relative	family relative + other	other relative	related	house-holds
	Farmer	1975	7	6	4	41	4	4	4	29	1
		1988	10	5	4	33	7	4	4	32	1
		1998	7	6	5	44	5	3	4	25	…
	Agricultural Salaried or Laborer	1975	36	9	1	31	8	2	1	8	6
		1988	25	6	7	26	13	2	5	10	6
		1998	31	10	2	32	6	1	2	13	3
	Unskilled Worker	1975	22	9	...	33	7	4	1	22	2
		1988	14	6	2	39	6	3	2	26	2
		1998	16	7	3	38	5	3	4	23	1
	Clerical Worker or Manager	1975	21	6	2	25	7	4	4	29	2
		1988	12	4	3	28	8	3	6	34	2
		1998	13	5	2	22	8	5	9	35	1
	Artisan or Petty Trader	1975	24	7	6	27	9	3	5	17	2
		1988	19	5	7	28	12	2	7	16	4
		1998	18	5	12	25	8	2	15	14	1
	Employer Or Professional	1975	30	5	5	27	6	3	2	20	2
		1988	22	5	6	28	10	2	4	20	3
		1998	8	2	3	26	4	2	8	45	2
	Inactive or Without Fixed income	1975	36	3	10	11	12	1	10	11	6
		1988	21	2	16	7	18	2	17	12	4
		1998	11	5	8	21	12	5	15	23	0
	Total	1975	16	7	4	34	6	3	4	24	2
		1988	14	5	6	29	9	3	6	26	2
		1998	11	6	6	35	6	3	7	25	1

Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National Household Living Sandards Survey of 1998.

Table 6

 6

	.5. Main types of household and presence of other relatives by three socioeconomic
		categories of (per 100 male-headed households)
			1975	1988	1998
	Agriculturalist	Isolated	7	10	5
		Monoparental	5	4	3
		Nuclear	84	80	88
		Extended	4	6	4
		Presence of other relatives	40,4	41,1	38,6
	Dominated	Isolated	33	27	20
		Monoparental	3	3	6
		Nuclear	56	57	68
		Extended	8	13	6
		Presence of other relatives	28,8	23,2	45,7
	Modern	Isolated	24	16	15
		Monoparental	2	4	4
		Nuclear	67	73	78
		Extended	7	7	4
		Presence of other relatives	38,1	37,1	51,3
	Total	Isolated	17	15	12
		Monoparental	4	4	4
		Nuclear	73	73	80
		Extended	6	8	4
		Presence of other relatives	37,5	35,7	44,1
	Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and
	from the National Household Living Sandards Survey of 1998.

Table 6 .

 6 6. Indicators of familial and social cohesion by socioeconomic group (in percent) Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National Household Living Sandards Survey of 1998.

			Persons living alone	Non related individuals	Other relatives	Children in nuclear households	Children in one-parent households	Children in one-parent households per
								1000 children
								in nuclear ones
	Farmer	1975	1,1	4,2	13,7	92,8	7,2
		1988	1,4	9,3	22,0	93,2	6,8
		1998	1,1	0,7	18,6	91,3	8,7
	Agricultural	1975	11,3	7,1	9,7	94,2	5,8
	Salaried or	1988	6,6	9,9	18,6	78,7	21,3
	Laborer	1998	9,0	1,8	13,4	87,7	12,3
	Unskilled	1975	5,0	4,5	14,5	98,0	2,0
	Worker	1988	2,6	7,2	14,2	96,9	3,1
		1998	3,0	1,9	17,3	92,4	7,6
	Clerical	1975	3,9	6,3	20,7	92,6	7,4
	Worker or	1988	1,8	10,0	20,6	91,4	8,6
	Manager	1998	2,1	3,4	28,2	91,3	8,7
	Artisan or	1975	5,4	5,8	15,4	85,3	14,7
	Petty Trader	1988	3,8	9,0	19,5	83,2	16,8
		1998	3,8	2,2	21,5	65,1	34,9
	Employer Or	1975	6,1	5,9	11,2	92,9	7,1
	Professional	1988	4,1	12,6	18,6	90,5	9,5
		1998	1,1	4,3	22,2	89,7	10,3
	Inactive or	1975	8,7	7,7	17,4	62,6	37,4
	Without	1988	4,1	11,8	31,8	48,9	51,1
	Fixed income 1998	1,8	3,0	30,0	76,3	23,7
	Total	1975	3,0	4,9	14,8	91,7	8,3
		1988	2,3	9,6	21,8	88,1	11,9
		1998	2,0	1,7	20,8	86,8	13,2

Table 6 .

 6 7. Ordered multinomial logistic regression of type of household by characteristics of the head, Côte d'Ivoire 1975

	Variable	Coefficient*	Std. Error	z-Statistic	p**
	Age	0.009551	0.006195	1.541545	0.1232
	Age 2	-0.000286	0,0000757	-3.771353	0.0002
	Marital status
	Married	4.881843	0.058998	82.74613	0.0000
	Separated, divorced, widowed	1.215001	0.102358	11.87013	0.0000
	Socioeconomic group
	Farmer	0.429065	0.085236	5.033864	0.0000
	Artisan or Petty Trader	0.145714	0.090864	1.603647	0.1088
	Clerical Worker or Manager	0.358368	0.083595	4.286966	0.0000
	Unskilled Worker	0.152187	0.083578	1.820895	0.0686
	Employer Or Professional	0.435927	0.115090	3.787692	0.0002
	Agricultural Salaried or Laborer	-0.231186	0.097402	-2.373524	0.0176
	Religion
	Muslim	-0.361699	0.050340	-7.185165	0.0000
	Christian	-0.185381	0.049944	-3.711753	0.0002
	Completed education
	None	-0.381800	0.071915	-5.309061	0.0000
	Secondary or higher	0.054020	0.078759	0.685894	0.4928

Table 6

 6

	.8. Ordered multinomial logistic regression of type of household by characteristics of the
		head, Côte d'Ivoire 1988
	Variable	Coefficient*	Std. Error	z-Statistic	P**
	Age	0.130300	0.013187	9.880640	0.0000
	Age 2	-0.001215	0.000134	-9.043403	0.0000
	Marital status
	Married	4.016149	0.147122	27.29809	0.0000
	Separated, divorced, widowed	0.399826	0.181024	2.208694	0.0272
	Socioeconomic group
	Farmer	-0.115038	0.138244	-0.832136	0.4053
	Artisan or Petty Trader	-0.405171	0.161881	-2.502899	0.0123
	Clerical Worker or Manager	0.007848	0.183784	0.042703	0.9659
	Unskilled Worker	-0.343257	0.157704	-2.176587	0.0295
	Employer Or Professional	0.382268	0.193807	1.972421	0.0486
	Agricultural Salaried or Laborer	-0.973482	0.230916	-4.215735	0.0000
	Religion
	Muslim	-0.299125	0.085368	-3.503954	0.0005
	Christian	0.018815	0.088078	0.213614	0.8308
	Completed education
	None	0.873384	0.962276	0.907623	0.3641
	Secondary or higher	0.320121	0.096933	3.302479	0.0010
	Note: See notes to table 7.

Table 6 .

 6 A1. Size of the population and number of households in the samples by socioeconomic group Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National Household Living Sandards Survey of 1998.

	Socioeconomic group		Population	Ménages
	Farmer	1975	110 528	16 877
		1988	141 543	20 492
		1998	11986	1887
	Agricultural Salaried or Laborer	1975	5 918	1 860
		1988	8 695	2 276
		1998	434	129
	Unskilled Worker	1975	20 604	4 718
		1988	17 189	3 199
		1998	2988	584
	Clerical Worker or Manager	1975	23 600	4 521
		1988	37 421	5 931
		1998	1980	317
	Artisan or Petty Trader	1975	14 741	3 287
		1988	32 231	6 664
		1998	3208	677
	Employer Or Professional	1975	6 163	1 271
		1988	6 084	1 031
		1998	1798	253
	Inactive or Without Fixed income	1975	8 204	1 995
		1988	25 103	4 786
		1998	2166	353
	Non-determined	1975	1 433	313
		1988	1 357	243
		1998	0	0
	Total	1975	191 191	34 842
		1988	269 623	44 622
		1998	24560	4200

Table 6 .

 6 A2. Mean age of heads of household, proportion of female heads and average size of household by socioeconomic group Sources : Micro-data from the 1975 and 1988 censuses of Côte d'Ivoire and from the National Household Living Sandards Survey of 1998. Note : *Only households of two persons or more.

	Socioeconomic group		Mean age	Female heads	Average size*
			(years)	(in per cent)
	Farmer	1975	36,2	4,8	7,0
		1988	44,9	7,3	7,5
		1998	45,5	11,4	6,8
	Agricultural Salaried or Laborer	1975	39,7	2,2	4,4
		1988	33,8	16,3	4,8
		1998	32,3	3,9	4,4
	Unskilled Worker	1975	38,9	0,6	5,3
		1988	36,7	0,4	6,3
		1998	38,0	7,9	5,9
	Clerical Worker or Manager	1975	40,6	5,0	6,3
		1988	35,2	8,2	7,1
		1998	39,1	12,9	7,0
	Artisan or Petty Trader	1975	38,0	15,8	5,6
		1988	37,0	18,7	5,9
		1998	38,9	31,5	5,5
	Employer Or Professional	1975	36,3	23,6	6,5
		1988	37,5	15,6	6,4
		1998	39,7	6,7	7,6
	Inactive or Without Fixed income	1975	42,4	31,7	5,9
		1988	44,0	58,2	6,2
		1998	55,7	30,3	6,8
	Non-determined	1975	37,9	7,4	6,4
		1988	41,0	15,1	6,8
		1998	43,0	15,3	6,5

Appendix The Ordered Multinomial Logistic Regression

The multinomial logistic model analyzes decisions concerning multiple choices, Y, that can be ordered. These choices are made by the individual i with multidimensional characteristics X i . In this model, choices Y i (where Y i goes from 0 to m) are related to a non-observable variable Y i *, which is linearly related to X i :

where b is a vector of parameters b j and u is a random vector of components that follow a logistic law. The value assumed by the random variable Y i * determines Y i according to the following rule: Y i = j when, and only when, c j < Y* < c j+1 .

The values c j are limits determining the thresholds of change of choice. The regression estimates parameters b j and c j . The sign of the coefficient b j gives the direction of the probability that the choice will be made in the extreme categories. For b j > 0, the corresponding explanatory variable indicates that the individual is more likely to choose Y i = m (and therefore less likely to choose Y i = 0). When b i < 0, however, the corresponding explanatory variable indicates that the individual is more likely to choose the smallest value of Y i (and therefore less likely to choose the largest value of Y i .).

Notes

1. On transformations of the family in developing countries, see the articles on Latin America, sub-Saharan Africa, the Arab world, and Asia in Burguière et al. (1986).

2. In this chapter, a nuclear family consists of a couple with or without children. Nuclearization is the tendency for the population to live increasingly in households consisting of such a nuclear family, whereas denuclearization would be characterized by a larger proportion of one-parent or single-person households.

3. The two censuses use the same definition based on de jure residence, whereas the survey definition introduces a criterion of duration. In 1975 and[START_REF] Locoh | L'évolution de la famille en Afrique[END_REF], the household was defined as "the group of persons, whether related or not, who acknowledge one individual entitled 'head of household,' and who hold part of their resources in common. They live in the same building." In 1998, however, the household was defined as "a group of persons who sleep usually in the same dwelling and who have shared their meals for at least three months during the 12 months that preceded the interview."

4. The household files were created with the SANDCO program [START_REF] Chevaugeon | SANDCO, système pour l'analyse des données collectives[END_REF]). Table 6.A1 in the Appendix gives the size of the population and the number of households by socioeconomic groups at the three dates.

5. The proportion of female heads of household in the survey of living standards is very close to that computed from the census data for the same year: 16 percent (Côte d'Ivoire n.d., 23).

6. The size reported in the survey on levels of living-5.79-was very close to that calculated on the basis of the census taken in the same year (Côte d'Ivoire n.d., 17).

7. In 1998, even more clearly than in 1975 or 1988, female heads of household were older than male heads (46.2 years versus 42.4) and had been responsible for the household for a shorter time, having reached headship at an older age than the men [START_REF] Fassassi | Le cycle de vie individuel au sein des ménages : différenciation selon les catégories socioprofessionnelles en Côte d'Ivoire[END_REF].

8. The "other relatives" include ascending and lateral relatives, grandchildren, and individuals allied by marriage to the head of household. 9. The last type, "head of household + non-related," is the only one for which the presence of non-related individuals is taken into consideration.

10. Farmers are self-employed agricultural workers. Agricultural wage earners and laborers include salaried workers of agro-industrial complexes and laborers earning wages or paid by the piece on village farms; their common trait is that they do not own the land on which they work. The "inactive or without fixed income" category includes individuals who are not currently in the labor force (students, unemployed, retired, and the like) and unpaid workers (for example, housewives, growers of food crops for home consumption, family workers, apprentices).

11. A summary table, 6.A2, in the Appendix gives the numbers of individuals and households for each socioeconomic group. Because the number of heads of household whose activity is unknown is not significant, the make-up of households in that category has not been presented in the text.

12. Farmers are only independent agriculturalists. The "dominated" include agricultural wage workers and laborers, artisans and petty traders, and the inactive or without fixed income. The modern category includes the other groups. The "isolated" type includes heads of household living alone or with non-relatives; the "one-parent" and "nuclear" types regroup the households of those types with and without non-relatives; the "extended" type includes all heads of households living with other relatives.

13. See the Appendix for a presentation of ordered multinomial logistic regressions. 14. Three kinship relationships are distinguished: between spouses, between parents and children, and between the head of household and another relative.

15. The classification was validated a posteriori as the values of the thresholds were all significantly different in 1975 as well as in 1998.

16. A distinction is made between categories 3 and 4, even though the number of kinship relationships is the same, because the nuclear family appears to be closest to the norm.


Ngoc Q K Duong
email: qduong@irisa.fr

Hideyuki Tachibana
email: tachibana@hil.t.u-tokyo.ac.jp

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

Nobutaka Ono

Rémi Gribonval
email: remi.gribonval@inria.fr

Shigeki Sagayama
email: sagayama@hil.t.u-tokyo.ac.jp

MULTICHANNEL HARMONIC AND PERCUSSIVE COMPONENT SEPARATION BY JOINT MODELING OF SPATIAL AND SPECTRAL CONTINUITY

Keywords: Harmonic and percussive source separation, local Gaussian model, continuity prior

This paper considers the blind separation of the harmonic and percussive components of multichannel music signals. We model the contribution of each source to all mixture channels in the time-frequency domain via a spatial covariance matrix, which encodes its spatial characteristics, and a scalar spectral variance, which represents its spectral structure. We then exploit the spatial continuity and the different spectral continuity structures of harmonic and percussive components as prior information to derive maximum a posteriori (MAP) estimates of the parameters using the expectation-maximization (EM) algorithm. Experimental results over professional musical mixtures show the effectiveness of the proposed approach.

INTRODUCTION

Sounds in most real-world musical mixtures can be classified into two major types depending on their spectral structure: harmonic sounds such as vocals, piano or violin and percussive sounds such as drums. Denoting by h(n, f ) and p(n, f ) the contribution of harmonic sounds and percussive sounds to all I mixture channels in the short time Fourier transform (STFT) domain in time frame n and frequency bin f , respectively, the observed I × 1 mixture signal x(n, f ) can be expressed as

x(n, f ) = h(n, f ) + p(n, f ).

(

) 1
The separation of these components from a mixture is useful for remixing [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF] and also for various music information retrieval tasks [START_REF] Durrieu | Singer melody extraction in polyphonic signals using source separation methods[END_REF][START_REF] Gillet | Transcription and separation of drum signals from polyphonic music[END_REF][START_REF] Tachibana | Melody line estimation in homophonic music audio signal based on temporal-variability of melodic source[END_REF]. In [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF] a method called Harmonic/Percussive Sound Separation (HPSS) was proposed whereby the harmonic and percussive sources can be blindly separated in the time-frequency domain from a single channel mixture using the assumption that spectrograms of harmonic components are smooth in the time direction while those of percussive components are smooth in the frequency direction. However, this technique does not exploit the spatial information available in multichannel mixtures and does not readily extend to this context due to the chosen divergence cost.

In this paper, we address the separation of harmonic and percussive components from multichannel mixtures using the local Gaussian modeling framework in [START_REF] Duong | Underdetermined reverberant audio source separation using a full-rank spatial covariance model[END_REF]. We model h(n, f ) and p(n, f ) as zero-mean Gaussian random variables whose respective covariances Σ h (n, f ) and

Σ p (n, f ) are factorized into Σ h (n, f ) = v h (n, f )R h (n, f ) Σ p (n, f ) = v p (n, f )R p (n, f ) (2)
where v h (n, f ) and v p (n, f ) are scalar time-varying spectral variances encoding the spectro-temporal power of harmonic and percussive components, respectively, while R h (n, f ) and R p (n, f ) are I × I full-rank time-varying spatial covariance matrices encoding their spatial position and spatial spread. Note that, compared to [START_REF] Duong | Underdetermined reverberant audio source separation using a full-rank spatial covariance model[END_REF], we do not assume that the spatial covariance matrices are constant over time. Rather, we introduce a continuity prior for the spatial covariance matrices and incorporate the temporal and spectral smoothness objectives in [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF] using different priors for the spectral variances of harmonic and percussive components. The parameters are then estimated in the maximum a posteriori (MAP) sense. Finally, the separated components are obtained in the minimum mean square error (MMSE) sense by multichannel Wiener filtering. Matlab code for the proposed algorithm is available 1 . The structure of the rest of the paper is as follows. We present the model of spatial and spectral continuity in Section 2 and address MAP estimation of the model parameters in Section 3. We provide experimental results to confirm the effectiveness of the proposed approach in Section 4 and finally we conclude in Section 5.

SPATIAL AND SPECTRAL CONTINUITY MODELING

Under the mixing model (1) and the parameterization (2), assuming that the components are uncorrelated, the vector of STFT coefficients of the mixture signal x(n, f ) is zero-mean Gaussian with covariance matrix

Σ x (n, f ) = v h (n, f )R h (n, f ) + v p (n, f )R p (n, f ). (3)
The log-likelihood is then given by

log L = - n,f tr(Σ -1 x (n, f ) Σ x (n, f ))+log det(π Σ x (n, f )) (4
) where det(.) denotes the determinant of a square matrix and Σ x (n, f ) the empirical mixture covariance matrix as defined in [START_REF] Duong | Underdetermined reverberant audio source separation using local observed covariance and auditory-motivated timefrequency representation[END_REF].

We enforce spatial and spectral smoothness of harmonic and percussive components by introducing prior distributions for R h (n, f ), R p (n, f ), v h (n, f ), and v p (n, f ), and estimating them in the MAP sense.

Spatial continuity prior

When each component consists of a single harmonic or percussive source and reverberation is moderate, the spatial covariance matrices are time-invariant and may be modeled as in [START_REF] Duong | Underdetermined reverberant audio source separation using a full-rank spatial covariance model[END_REF]. However, in general, each component consists of several sources, e.g the percussive component includes several drums (bass drum, snare drum, hi-hat, etc). The spatial covariance matrices of each component are then time-varying but can be assumed to vary smoothly over time due to the fact that one source usually predominates in a given time-frequency neighborhood. We then choose the following Markov chain prior for R h (n, f ) and

R p (n, f ) when n > 1 p R h (n, f ) = IW R h (n, f )|(m h -I)R h (n -1, f ), m h p R p (n, f ) = IW R p (n, f )|(m p -I)R p (n -1, f ), m p .
(5) IW R|Ψ, m denotes the inverse Wishart density over positive definite matrices R with positive definite inverse scale matrix Ψ and m degrees of freedom [START_REF] Maiwald | Calculation of moments of complex Wishart and complex inverse-Wishart distributed matrices[END_REF]

IW(R|Ψ, m) = |Ψ| m |R| -(m+I) e -tr(ΨR -1 ) π I(I-1)/2 I i=1 Γ(m -i + 1) (6)
with tr(.) denoting the trace of a square matrix and Γ the Gamma function such that the mean of R is given by Ψ/(m-I) [START_REF] Maiwald | Calculation of moments of complex Wishart and complex inverse-Wishart distributed matrices[END_REF]. This distribution, its mean, and its variance exists for m > I -1, m > I, and m > I + 1 respectively The reason for which we consider an inverse-Wishart prior for the spatial covariance matrices is that it is the conjugate prior for the likelihood of the considered Gaussian observation model, which results in closed-form updates. The initial distributions p R h (1, f ) and p R p (1, f ) are chosen as uniform for all f .

Spectral continuity prior

Since the spectrum of harmonic components is usually smooth over the time axis while that of percussive components is usually smooth over the frequency axis [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF], we consider the following Markov chain priors for v h (n, f ) with n > 1 and v p (n, f ) with f > 1:

p v h (n, f ) = IG v h (n, f )|α h , (α h -1)v h (n -1, f ) p v p (n, f ) = IG v p (n, f )|α p , (α p -1)v p (n, f -1) (7
) IG(v|α, β) denotes the inverse-gamma density with shape parameter α > 0 and scale parameter β > 0

IG(v|α, β) = β α Γ(α) v -α-1 e -β/v ( 8
)
whose mean is β/(α -1).

Similarly to the choice of initial distribution for the spatial covariances, p v h (1, f ) ∀f and p v p (n, 1) ∀n are chosen as uniform. The choice of an inverse-gamma prior, which is the conjugate prior for the considered likelihood, brings not only simpler computation compared to the Gaussian prior in [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF] but also better separation performance as shown in our experiments in Section 4. This prior distribution was also used to model temporal continuity in [START_REF] Févotte | Nonnegative matrix factorization with the Itakura-Saito divergence. With application to music analysis[END_REF] in the different context of multipitch estimation.

MAP ESTIMATION OF MODEL PARAMETERS

We derive an EM algorithm to estimate the spatial parameters θ spat = {R h (n, f ), R p (n, f )} n,f and the spectral parameters θ spec = {v h (n, f ), v p (n, f )} n,f of the two types of components in each time-frequency bin (n, f ) using the complete data c = {h(n, f ), p(n, f )} n,f , that is the set of STFT coefficients of the harmonic component and the percussive component in all time-frequency bins.

In the E-step, the expected covariance matrices Σ h (n, f ), Σ p (n, f ) are updated similarly as in [START_REF] Duong | Underdetermined reverberant audio source separation using local observed covariance and auditory-motivated timefrequency representation[END_REF] using the Wiener filters W h (n, f ) and W p (n, f )

W h (n, f ) = Σ h (n, f )Σ -1 x (n, f ) (9)
W p (n, f ) = Σ p (n, f )Σ -1 x (n, f ) (10)
Σ h (n, f ) = W h (n, f ) Σ x (n, f )W H h (n, f ) (11) + (I -W h (n, f ))Σ h (n, f ) Σ p (n, f ) = W p (n, f ) Σ x (n, f )W H p (n, f ) (12)
+ (I -W p (n, f ))Σ p (n, f )
where I is the I × I identity matrix, Σ h (n, f ), Σ p (n, f ) are defined in (2), Σ x (n, f ) in (3), and Σ x (n, f ) in [START_REF] Duong | Underdetermined reverberant audio source separation using local observed covariance and auditory-motivated timefrequency representation[END_REF].

In the M-step, the auxiliary function Q defined in the MAP sense as

Q M AP (θ|θ old ) = log p c|θ + γ 1 log p θ spat +γ 2 log p θ spec ( 13
)
is maximized with respect to the parameters θ = {θ spat , θ spec }, where γ 1 , γ 2 are tradeoff hyper-parameters determining the contribution of the priors and

p c|θ = n,f p h(n, f )|0, Σ h (n, f ) p p(n, f )|0, Σ p (n, f ) (14)
p θ spat = n,f p R h (n, f ) p R p (n, f ) (15)
p θ spec = n,f p v h (n, f ) p v p (n, f ) . (16)
By substituting ( 5) into (15), ( 7) into (16), and ( 14), ( 15), ( 16) into (13), then computing the gradient of Q M AP (θ|θ old ) with respect to each entry of R h (n, f ), R p (n, f ) and equating it to zero, we obtain a quadratic matrix equation. After solving this equation under the constraint that the solution is positive definite [START_REF] Higham | Solving a quadratic matrix equation by Newton's method with exact line searches[END_REF], the spatial covariance matrices are updated as

R h (n, f ) = (1/2)A -1 h -B + (B 2 -4A h C h A h ) 1/2 A -1 h R p (n, f ) = (1/2)A -1 p -B + (B 2 -4A p C p A p ) 1/2 A -1 p
(17) where (.) 1/2 denotes the square root of a Hermitian matrix, and

A h = γ 1 (m h -I)R -1 h (n + 1, f ) 1/2 A p = γ 1 (m p -I)R -1 p (n + 1, f ) 1/2 B = (γ 1 I + 1)I (18) C h = -Σ h (n, f )/v h (n, f ) -γ 1 (m h -I)R h (n -1, f ) C p = -Σ p (n, f )/v p (n, f ) -γ 1 (m p -I)R p (n -1, f )
Similarly, by computing the gradient of Q M AP (θ|θ old ) with respect to v h (n, f ), v p (n, f ) and equating it to zero, we get a second order polynomial form of the source variances with a single positive solution, that is

v h (n, f ) = (-b + √ b 2 -4a h c h )/(2a h ) v p (n, f ) = (-b + b 2 -4a p c p )/(2a p ) ( 19
)
where

a h = γ 2 (α h -1)/v h (n + 1, f ) a p = γ 2 (α p -1)/v p (n, f + 1) b = γ 2 + I (20) c h = -tr R -1 h (n, f ) Σ h (n, f ) -γ 2 (α h -1)v h (n -1, f ) c p = -tr R -1 p (n, f ) Σ p (n, f ) -γ 2 (α p -1)v p (n, f -1)
Note that, in ( 18) and ( 20), due to the choice of initial distributions R h (n -1, f ), R p (n -1, f ), v h (n -1, f ) are zero for all f when n = 1, and v p (n, f -1) is zero for all n when f = 1. Source variances are uniformly initialized as v h (n, f ) = v p (n, f ) = 1 for all n, f while the spatial covariance matrices are initialized from the observed mixture covariance as R h (n, f ) = R p (n, f ) = 1 2 Σ x (n, f ) ∀n, f . The algorithm converges just after five EM iterations. Finally, the separated components are obtained by multichannel Wiener filtering as

h(n, f ) = W h (n, f )x(n, f ) p(n, f ) = W p (n, f )x(n, f ) (21)

EXPERIMENTAL RESULTS

Sound mixing techniques vary depending on the music genre: for certain genres, instruments are placed at different spatial positions while for other genres they are all mixed to the center. We evaluated the separation performance of the proposed algorithm over 8 stereo music mixtures of harmonic and percussive sources corresponding to two different mixing conditions. These mixtures are part of the Quaero project database, which was used for the Professionally produced music recordings task of the 2010 Signal Separation Evaluation Campaign (SiSEC 2010) 2 . The first 4 mixtures were originally mixed by a sound engineer where most instruments are panned close to the center with artificial reverb, and the total number of harmonic and percussive sources in each mixture varies from four to eight. In order to investigate the contribution of spatial information, in the second set of mixtures (named Pan+) we moved each source to a random position by amplitude panning but keeping the same reverb. The parameter setting is summarized in Table 1. In this experiment, the empirical mixture covariance Σ x (n, f ) was computed by local averaging as in [START_REF] Duong | Underdetermined reverberant audio source separation using local observed covariance and auditory-motivated timefrequency representation[END_REF] and the hyper-parameters m h , m p , α h , α p are heuristically fixed depending on the desired shape of the priors, which determines the degree of smoothness. Separation performance was evaluated using the widely used signal-to-distortion ratio (SDR) criterion measuring the overall distortion, as well as the signal-to-interference ratio (SIR), signal-to-artifact ratio (SAR) and source imageto-spatial distortion ratio (ISR) criteria in [START_REF] Vincent | First Stereo Audio Source Separation Evaluation Campaign: Data, algorithms and results[END_REF]. We compared the performance of the proposed multichannel har-monic and percussive sound separation algorithm (M-HPSS) with that achieved by the original single channel HPSS algorithm using I-divergence and Gaussian continuity priors (HPSS) [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF], and with that given by the single channel HPSS algorithm introduced in this paper using inverse-gamma prior (HPSS IG ). The results were averaged over all mixtures for each dataset and are shown in Table 2. All mixtures and the harmonic/percussive signals separated via the 3 tested methods are available on our webpage 3 The numerical results show the significant separation improvement of HPSS IG compared to the original HPSS in terms of all criteria over both datasets. This means that the inverse-gamma prior investigated in this paper better models the spectral continuity of harmonic and percussive components than the Gaussian prior introduced in [START_REF] Ono | A real-time equalizer of harmonic and percussive components in music signals[END_REF]. Separation performance given by HPSS and HPSS IG over the Pan+ dataset is very similar to that over the original dataset due to the fact that panning does not affect the spectral structure of the sources. But the performance achieved by M-HPSS has noticeably increased in panned datasets, i.e. the SDR is 0.6 dB higher than that given by HPSS IG showing the benefit of exploiting spatial information. The performance improvements are confirmed by informal listening test and by the additional auditory-motivated criteria introduced at SiSEC 2010.

CONCLUSION

In this paper, we proposed a multichannel approach for the separation of harmonic and percussive components in musical recordings by joint modeling of spatial and spectral continuity. We investigated suitable continuity priors for both spatial and spectral parameters such that they are estimated in the MAP sense using the EM algorithm. Experimental results over professional musical mixtures confirm the benefit of the proposed multichannel approach compared to singlechannel algorithms. Future work will investigate the learning of hyper-parameters and consider the proposed separation algorithm as a pre-processing step for some MIR tasks, e.g. singing voice extraction.

Table 1 .

 1 Common experimental parameter settings

	Mixture signal duration	10 s
	Number of channels	I = 2
	Sampling rate	44100 Hz
	STFT frame size	4096
	STFT frame shift	2048
	Number of EM iterations	5
	IG shape parameters	α h = α p = 10
	IW degrees of freedom	m h = m p = 5
	Trade-off parameters	γ 1 = 0.5, γ 2 = 1

Table 2 .

 2 . Average harmonic/percussive component separation performance

			SDR SIR SAR ISR
		HPSS	3.8	5.2	7.6	8.7
	Original	HPSS IG	4.8	7.9	8.0	10.7
		M-HPSS	5.0	7.2	8.6	10.1
		HPSS	3.8	5.1	7.5	8.6
	Pan+	HPSS IG	4.7	7.7	8.2	10.4
		M-HPSS	5.3	7.4	8.8	10.3

https://www.irisa.fr/metiss/ngoc/sw/hpss.rar

http://sisec.wiki.irisa.fr/

https://www.irisa.fr/metiss/ngoc/sw/HPSSresults.rar

ACKNOWLEDGMENT

This work was supported by INRIA under the Associate Team Program VERSAMUS (http://versamus.inria.fr).


Frédéric Garnier

Hervé Lesueur

Mikael Motelica-Heino

Ioannis Ignatiadis

AQUIFER BIOTHERMOREMEDIATION USING HEAT PUMPS: SOUND THEORETICAL BASIS AND RESULTS ON THERMAL, GEOCHEMICAL AND BIOLOGICAL IMPACTS ON AQUIFERS

Geothermal heat pumps have been operated on aquifer over the past thirty years. Currently, these systems constitute a major sector of renewable energy development. However, this development is accompanied by several difficulties at scientific, technical and administrative levels, to describe short and long term interactions with aquifers, at both the local and regional scale, especially close to urbanized or industrialized areas.

As a typical example, the long-term use of groundwater heat pumps for air conditioning of homes or buildings can induce significant increases in temperature of the aquifer, if, for given groundwater flow direction and rate, there is an imbalance between the demands for cooling and heating. Therefore, the aquifer (groundwater and sediments) can be affected. In fact, it is expected that a wide variety of geochemical reactions and microbiological changes with variable intensity should occur which depends on the sediment characteristics and hydrogeological background. The presence of organic pollutants in the aquifer can amplify these phenomena. The predictable results may progressively be: (i) precipitation, which reduces the porosity of the aquifer and/or the well productivity, (ii) an inappropriate temperature for the use of groundwater heat pumps for air conditioning, but also and especially (iii) pollutant bioremediation, which has a beneficial impact on the aquifer. Under certain conditions, this bio-thermo-remediation can be considered as an attractive option for some contaminated aquifers, taking into account the fact that, administratively in European countries, any action is subject to authorization.

Notably in the framework of the collaborative project BIOTHERMEX (French Region Centre, convention n° 200800034163), exploratory studies were focused on three objectives: i) Improving the understanding of the concept of bio-thermo-remediation of aquifers by using effects induced by geothermal heat pumps. ii) examining realistic configurations, on a laboratory scale, pilot-scale and in-situ, in order to identify the most determining factors for possible (undesirable or helpful) aquifer impacts, e.g. temperature increase, bacterial development, organic pollutants degradation iii) evaluating if those configurations can present interests for bio-thermo-remediation of polluted aquifers by using heat pumps.

A literature survey led to the consolidation of the basic principles of bio-thermo-remediation of most organic pollutants: increase in volatilization, solubility, degradation kinetics and mobility of the residual pure phases by reduction of their viscosity. The different heat pump systems and processes are discussed in the article, to identify what is suitable for biothermo-remediation.

To reproduce the underground thermal conditions encountered in groundwater heat pumps systems (temperature range of water production from 10 to 25 °C, temperature range of water injection between 20 and 35 °C), batch-experiments, at laboratory and pilot scale have been carried out to investigate the impacts of the different parameters on the geochemical equilibrium (solubility, mobility, precipitation, dissolution, volatilization,) on the aquifer inorganic content and organic pollutants as well as on microbial populations activities. Two different sediments were used. Depending on the nature of the sediments and the water composition, the impacts are more significant: (i) thermally, with a low water flow rate, (ii) geochemically, with the high bicarbonate and Ca/Mg contents in water and (iii) biologically, with a organic contaminants contents in water. Some results from in-situ measurements (especially with an aquifer polluted by chlorinated solvents) are used to corroborate the conclusions. Even if the most part of the work is still in progress, the obtained results are validated by biogeochemical modelling.

The combination of a low-enthalpy geothermal system using aquifer heat pumps (water pumping and re-injection) and remediation approaches appears to be an appropriate method to treat aquifers polluted by organic contaminants without use of any other way than the thermal energy.

Key words: aquifer heat pumps, remediation, pollution, thermal enhancement, precipitation, biothermoremediation.

THEORETICAL AND BIBLIOGRAPHICAL BASIS ON THE REMEDIATION BY THERMAL ENHANCEMENT, PARTICULARLY BY GEOTHERMAL HEAT PUMPS

The use of geothermal energy is today promoted as an alternative and sustainable source of energy. While Geothermal Heat Pumps (GHPs) are operational on aquifers over the past thirty years, today they always constitute a major sector of renewable energy development. However, regarding the authorization, regulation and monitoring of such facilities with respect to possible environmental impacts, a severe lack of knowledge has been identified [START_REF] Brielmann | Effects of thermal energy discharge on shallow groundwater ecosystem[END_REF]. Thus, the development of GHPs is accompanied by difficulties in scientific, technical and administrative levels, to describe interactions with aquifers, short and long term as to the local or regional scale, especially close to urban or industrialized areas. Aquifers are not only abiotic reservoirs of water and sediment, but they are complex ecosystems harboring an almost unexploited diversity of microorganisms and fauna. Intrinsic groundwater microorganisms are highly adapted to extremely oligotrophic, but stable conditions including temperature. At the same time, groundwater biotas are the key drivers of important ecosystem services, especially functions connected to water quality.

Examples to demonstrate what was previously presented exist. An example is that the long-term use of GHPs for air conditioning of homes or buildings can induce important increases in temperature of the aquifer, if, for a given groundwater flow direction and rate, there is an imbalance between the demands for cooling and heating. This is the case in the urban and industrialized area of Lyon City (France), where the GHPs density caused a permanent temperature increase sometimes higher than 10°C. Therefore, in such a case the aquifer (groundwater and sediment) can be affected. In fact, it is expected that should occur a wide variety of geochemical reactions and microbiological developments with variable intensity which depends on the groundwater and sediment characteristics and hydrogeological background (type of aquifer, hydraulic conductivity, etc.).

GHPs functioning on aquifer are likely to cause the following predominant problems [1-2-6]: (i) disturbance of the thermal or hydraulic behaviour of the aquifer which may affect the suitability of groundwater for further use (interference for nearby users) (ii) precipitation of mineral species, which may reduce the porosity of the aquifer and/or the well productivity (clogging of heat exchangers, scaling on pipes). Dominant scaling product are expected to be calcium carbonate (supersaturation at elevated temperature and/or stripping of carbon dioxide from groundwater) and iron or manganese oxy-hydroxides (microbiological processes, corrosion by-product). (iii) decrease of dissolved gas saturation (oxygen, carbon dioxide), mobilization of organic matter, silica reactions (iv) ecological changes in the target groundwater which could lead to detrimental or beneficial effect on activities, diversity, growth and survival of biological species, especially bacterial community. Until now, insufficient data precluded the estimation of the response of an aquatic system to increased water temperature, including study related to health aspects.

In addition, the presence of organic pollutants in the aquifer can amplify these phenomena. This could, in case of appropriate temperature condition, enhance the biodegradation of organic pollutants or pollution bioremediation, which is a beneficial impact for the water quality of the aquifer. Under certain conditions, this bio-thermo-remediation of soils and aquifers, polluted by organic compounds, can be considered an attractive option for some contaminated aquifers, taking into account the fact that, administratively in European countries, any action is subject to authorization [START_REF] Hiester | Technical Scale Investigations for the insitu Remediation of Low Volatile Contaminants by Thermal Wells[END_REF].

The policy of spreading out of the cities is not any more topicality and the strong current land pressures lead to the rehabilitation of the industrial waste lands, as well as the requirement to give access to clear water and a healthy environment. In order to contribute to the restoration of the industrial waste lands polluted by organic pollutants the use of low enthalpy geothermal energy processes, normally dedicated to the heating and the air-conditioning of the buildings, is often cited in the literature as a key issue.

The main organic pollutant addressed by this "thermally enhanced" remediation are (i) light aliphatic hydrocarbons, Volatile Aromatic compounds (VAC), Volatile Organo-Halogenated Compounds (VOHC), and some dicyclic Aromatic Hydrocarbons (naphthalene and its alkylated derivatives), which are among the most problematic pollutants to manage.

Using, either GHPs directly on aquifers or indirectly with vertical geothermal probes, both in the unsaturated and saturated zone, leads to an increase of the ground temperature. This increase in temperature can enhance the organic compounds recovery and degradation. Thus, for the above mentioned organic compounds (and more specifically for the CAV and COHV), an increase in temperature of the aquifer (groundwater and sediment) can cause [3-4-8-9]: (i) an increase in volatilization, (ii) an increase in solubility, (iii) an increase in degradation kinetics and (iv) an increase in mobility of residual pure phases by reduction in their viscosity.

The positioning of the bio-thermo-remediation is thus halfway between the traditional in situ thermal desorption and the traditional extractive methods used for VOHC (pump and treat, venting, dynamic biostimulation). In addition, the fact to moderately increase the temperature will lead to a biostimulation. Thus, the intermediate positioning of this new in situ technology for remediation and reconversion of industrial polluted lands will make it possible to benefit from the advantages of each above-mentioned technique.

If we consider the biothermoremediation as a treatment process, then the temperature increase of the aquifer can cause: (i) a reduction of treatment duration;

(ii) reduction of the energy impact of the operation of depollution, energy necessary to the thermal increase being provided by a renewable energy to very weak impact in terms of emissions; (iii) reduction in the treatment costs in comparison to the traditional desorption techniques, because a) of a mutualisation of the material of desorption heating/depollution) and b) of a technique less energy consuming that traditional desorption; (iv) less impact on the quality of the groundwaters and the micro-organisms that traditional thermal desorption.

A literature survey has led to the consolidation of the basic principles of bio-thermo-remediation mainly known as "thermal enhancement" of most organic pollutants. The different GHPs systems and processes are discussed in this survey, to identify the most suitable for bio-thermo-remediation. A final technical and economical appraisal will enable to rate the technologies on the current remediation market and to determine its optimal range of application with respect to currently used technologies. Through demonstrating the performance of the "thermal treatment", the expected impacts shall be to promote the implementation of processes coupling remediation and energy taking into account technical, economic and social aspects. This diversion of the traditional use of these renewable energies fits in a "life cycle thinking" approach, which is been developed at the European level, when regarding how we conceive the development, and therefore how to rehabilitate the brownfield sites. The thermal enhancement is trying to gain a sustainable production foothold and it promotes also a minimization of the impacts by using green energy, and thus shows a will to develop the pathway of a "green depollution ".

CONTEXT AND OBJECTIVES OF THE PRESENT WORK

Bacterial communities play an essential role in aquatic ecosystems. They are responsible for much of the cycling of both carbon and nutrients. In groundwater, these communities often dominate the biotas, both in biomass and in metabolism. Temperature is known to be a key factor for the growth and the development of microorganisms. More commonly, any species have a range of tolerance on temperature condition, the so-called "cardinal temperature", with an upper and lower limit for growth and an optimum temperature at some point of these two extremes. Although the effect of temperature on individual taxa is well studied, the effect of temperature on the metabolism of natural bacterial communities is poorly understood in terms of community composition, resources acquisition (metabolism), interaction between species etc. Most of the bacterial species in groundwaters are adapted to a relatively narrow temperature regime and we could ask how the artificial temperature discharge can affect bacterial metabolism.

Notably, in the framework of the collaborative project BIOTHERMEX (French Region Centre, convention n° 200800034163), exploratory studies were focused on two main objectives:

(i) examining realistic configurations, on a laboratory scale, pilot-scale and in-situ, in order to identify the most determining factors for possible (undesirable or helpful) aquifer impacts, e.g. temperature increase, bacterial development, organic pollutants degradation (ii) evaluating if those configurations can present interests for bio-thermo-remediation of polluted aquifers by using GHPs and improve understanding of the concept of bio-thermo-remediation of aquifers by using effects induced by GHPs.

Attempts to attain a metabolism limit by both temperature and substrate is proposed experimentally in this study. Therefore, the main goal of our research is to understand the relationships between temperature, substrate content and microbial activity during Aquifer Thermal Energy Storage (ATES), and quantify the effect on microbial activity of a groundwater used for geothermal applications.

MATERIAL AND METHODS

Groundwater collection

In order to evaluate the metabolic activity, two different sites are used to collect groundwaters. The first site, situated in Balandran (Gard, southern France) is taken for reference. There, non-polluted groundwater is periodically used for cooling or heating of agricultural greenhouses. Three main piezometers surrounding the production and injection wells of this site are equipped with temperature probes in different depths. Their groundwaters are periodically sampled and analyzed during a year. The groundwaters were sampled with a submersible pump from a depth of 12 m and were collected in sterile bottle with aseptic procedure for microbial analysis. The non-conservative water parameters are: pH 6.79 at 16.4°C, electrical conductivity 560µS/cm (at 25°C), pe 7.02, dissolved oxygen 7.24 mg.L -1 and alkalinity 3.88 mmol.L -1 . The total organic carbon and the dissolved organic carbon (DOC) were both equal to 0.7 mg.L -1 . The concentrations of the main inorganic ions (in mM) were: Ca 2+ 2.76; Na + 0.64; Mg 2+ 0.32; Cl -0.82; NO 3 -0.67; SO 4 2-0.79. The second site is situated in the urban and industrialized area of Lyon city (in modern fluviogenic soils), where the GHPs density is so high that groundwater temperature is thermally and quasi-permanently altered. In addition, the site is polluted by organic compounds and there are four GHPs that are using important flow rates (>50 m 3 /h) for cooling (reject hot water). The site is monitored over several years. In the field, the main non conservative parameters are measured and after sampling, the main organic pollutants are quantified according to EN ISO 10301 for VOHV, EN ISO 9377-2 for hydrocarbon oil Index; ISO 11423-1 for VAC, and NFT 90-115 for PAH.

Metabolic activity evaluation

Two approaches are used to examine the temperature effect on bacterial metabolic activity (enzymatic activity) of groundwater from Balandran: the deshydrogenase activity and the carbon source utilization profile.

Deshydrogenase activity approach

The 2-(p-iodophenyl)-3-(p-nitrophenyl)-5-phenyl tetrazolium chloride (INT) was used to measure dehydrogenase activity (respiratory activity). The INT assay is not commonly performed on water as sample, that's why the method has been modified to facilitate the analysis of water. The following steps outline a filtration procedure that traps bacteria on a nylon membrane thereby concentrating them from 100 ml of groundwater. The membrane containing the bacteria is then incubated into a 0.02% INT solution for 4 days in 3 replicates at controlled temperature. Extraction of formazan was made in vials containing 10 ml of acetone. The INT-formazan extract was then measured by spectrophotometry (wavelength adjusted at 480 nm).

Carbon source utilization profile approach

ECOLOG plates (AES Lab, France) were used in order to evaluate the effect of incubation temperature on carbon substrate utilization rate and pattern. Plates were inoculated with 150 μl of whole groundwater samples and incubated in the dark at different temperatures. Each well in these manufactured 96-well microplates contains lyophilized nutrients and a tetrazolium redox dye (triphenyletetrazolium chloride, TTC) as well as one of the 31 carbon source. Oxidation of the carbon source is indicated by colorimetric reduction of the dye. Following incubation, absorbance of the colorimetric reaction was monitored every 24 h for 1 week with a plate spectrometer (Multiskan spectrum, ThermoLab system). Average Well Color Development (AWCD) was calculated and the data was standardized by subtracting the blank control well measure from each substrate. The carbon source utilization profiles were conducted in six replicate samples of each incubation temperature. In laboratory conditions, only the metabolic activities of groundwater from Balandran (a reference non-polluted groundwater) were evaluated. The impact of the temperature incubation on substrate degradation could be detected as shown in figures 1 and 2 which present respectively the results of the respiratory activity and ECOLOG approaches.

Results indicate an immediate and significant effect of temperature on GW bacterial communities. As temperature increase, the rate of chemical reactions (carbon mineralization) increases until an optimum temperature is reached.

If the temperature reaches 36°C, there is a sharp decrease in metabolic activities. The low-temperature has the effect of slow down the bacterial activities. The reasons for the upper limit of temperature tolerance are relatively well understood, determined by the denaturation of key cellular components, which disrupt the cellular function. For the ECOLOG approach (figure 2), there is no further observable effect of temperature on the quality of substrate degradation (data not shown). The presence of substrate seems not to overrides temperatures effect. The non-polluted groundwater of Balandran is periodically extracted for cooling or heating of agricultural greenhouses. Two production-injection wells and three other piezometers, monitored during one entire year, revealed only a slight thermal effect that decreases as a function of the depth and the distance from the injection well (results will be shown in the oral presentation). In addition, no significant geochemical or microbiological disturbance was still evidenced. Nevertheless, in the paragraph 4.1 was demonstrated that the situation will be other and predictable in the longer term, especially if the water table was reached by an organic pollution.

Thermal and geochemical perturbations on a site in Lyon city

The evolution, over 5 years of monitoring, of the main geochemical parameters and some sensitive ions, and of the organic compounds contents has evidenced that the Lyon site is thermally and geochemically perturbed and partly remediated (results will be shown in the oral presentation). In the groundwater the pH and redox potential were decreased, the dissolved oxygen content was made null; temperature, conductivity and ion chloride content were increased (by reductive dechlorination). Concentrations of all classes of organic compounds (especially those of VOHC and VAC) decline for more than 80 %. Even if the most part of the work is still in progress, the obtained results corroborated the predictable consequences: (i) an inappropriate temperature increase for further use of groundwater by heat pumps for air conditioning and (ii) biodegradation of organic pollutants or pollution bioremediation, which is a beneficial impact for the water quality of the aquifer.

CONCLUSIONS AND PERSPECTIVES

Understanding how thermal discharge affects bacterial community processes, and thus ecosystem processes, is one of the challenges of BIOTHERMEX project. The main issue is what happens if groundwater biotas need to cope with sudden temperature dynamics caused by GHPs use. Potential effects of thermal use on groundwater systems already facing enhanced loads of nutrients or contamination require urgent scientific attention.

Within this project, we have assessed, both in the laboratory and in the field, the impacts of temperature discharge and withdrawal on biotic parameters and functional characteristics of exemplary shallow groundwater systems.

We have examined how heterotrophic bacterial communities respond to temperature by two experimental approaches. These preliminary results confirm the predictable effect of temperature on bacterial activities and provide insight into the effect of temperature limitation for bacterial metabolism (loss of biological function represented by carbon mineralization). Temperature is also an important limiting factor for ecological processes. Bacterial communities represent thus sensitive informative indicator to understanding the potential impact of thermal energy discharge in groundwater ecosystem. Additional research is devoted to evaluate how the temperature will affects the population dynamics (e.g. genetic structure and density) and to estimate the degree of adaptation of the communities to higher temperature and the consequence on ecosystem processes.

The combination of a low-enthalpy geothermal system using aquifer heat pumps (water pumping and re-injection) and remediation approaches appears to be an appropriate method to treat aquifers polluted by organic contaminants without use of any other products than the thermal energy.

Figure 1 :

 1 Figure 1: Effect of temperature and substrate addition on deshydrogenase activity of Balandran groundwater.

Figure 2 :

 2 Figure 2: Impact of both temperature and incubation time on substrate mineralization (ECOLOG approach) of Balandran groundwater 4.2. Thermal, geochemical and microbiological perturbations on Balandran site

Table 1 :

 1 Substrates in Biolog® Ecoplate

4. RESULTS AND DISCUSSION

4.1. Effect of temperature on groundwater bacterial communities from Balandran

ACKNOWLEDGEMENTS

This ongoing work (hal-00593563) is supported by the collaborative project BIOTHERMEX (French Region Centre, convention n° 200800034163) and receives financial support by BRGM research division.