Writing the Fragmented City: Black Neighborhoods in Dawn Turner Trice's Only Twice I've Wished for Heaven

Break a vase and the love that reassembles the fragments is stronger than the love which took its symmetry for granted when it was whole. The glue that fits the pieces is the sealing of its original shape.

-Derek Walcott, The Antilles Chicago-born Dawn Turner Trice belongs to a new, emerging generation of black female writers. Her debut novel Only Twice I've Wished for Heaven (1997) has met with great critical acclaim and reviewers agree that it "adds a new perspective to the urban African American experience" . Set in the "Windy City" in 1975, the novel contrasts two black neighborhoods separated by a fence: Lakeland, a planned community that shelters a new black bourgeoisie, and Thirty-fifth Street, a microcosm of the decaying ghetto. Through the central characters of eleven-year-old Temmy Saville (a new resident in Lakeland who often runs off and crosses over to Thirty-fifth Street) and Jonetta Goode (a former prostitute on Thirty-fifth and a liquor-store owner reaching sixty, but also a protector and guiding force for young Temmy), the author shows how racial and social segregation affects the lives of black city-dwellers. Only Twice is a coming-of-age novel about self-positioning and belonging. It ends tragically with the death of a child, Temmy's friend and Jonetta's greatniece Valerie. The author interweaves the two first-person narratives of Temmy and Jonetta, some twenty years after the events.

Trice's fictional cartography of black Chicago as a dual, fragmented cityscape is pregnant with meaning. My purpose is to examine the narrative strategies that the author uses in her figurative representation of urban and architectural space. I will expose how Dawn Turner Trice gradually deconstructs upscale Lakeland as utopia while she reconsiders the underprivileged inner-city neighborhood as the "urban village" with the formative presence of the "ancestor."

For Temmy's father, leaving South Morrison Street on the South Side to move to Lakeland is "a once-in-a-lifetime opportunity" (16), and Temmy's initial description of the place proves him right:

[The guard] handed him a map and showed us how to maneuver Lakeland's labyrinth of twists and turns to the Five forty-five building, our new home. Finally, he opened a massive iron gate that groaned as it parted, and we were allowed in. […] This place was straight out of a fairy tale. One square mile of rich black soil carved out of the ghetto. One square mile of ivory towers, emerald green grass, and pruned oaks and willows so stately, they rivaled those in the suburbs […]. The four high-rise apartment buildings were the tallest structures I'd ever seen, and already janitors were hanging from scaffolds, washing beveled-glass windows, making sure everything shined in tandem. (18)(19) With its guarded iron gate, Lakeland appears as a safe haven, a fortified enclave resisting against street crime and urban poverty. Constructed in an orderly fashion as a garden sanctuary within the city, the lavish estate radiates peacefulness and harmony. Its majestic trees, rooted in a rich soil, suggest vitality, anchorage and permanence; its winding streets, evocative of country roads, break with the monotonous rigid grid map of downtown Chicago and contribute to this pastoral scenery. The serenity of landscaping and architecture makes this residential area a soaring space. Unquestionably, Trice uses the verticality of the massive apartment buildings as a metaphor for upward mobility and retrenchment. The author's references to size, acreage, and height set the cityscape in perspective, thereby giving a sense of depth and volume suggestive of the community's lofty ideals and ambitions: "It was an idyllic community, stripped of limitations and bounds" (19). Lakeland, a monolithically black neighborhood within a restricted area, built on the shore of Lake Michigan, brings together the seductive closeness of a cocoon and the openness of outer space. The very name of the place alludes to its spatiality. Lakeland is a borderland facing a wilderness of water; it is a new Frontier, a conquered space of freedom that bears promises.

Once allowed in, the Savilles discover a new world, an unknown territory. Yet, thanks to the map that gives them structure and a sense of direction, they can navigate through the maze of streets, through the many possibilities now offered to them. For the longest, even the city had wanted to forget it was there. The mayor started by taking every city map and drawing a row of X's on the grid line between Thirty-fourth and Thirty-sixth streets.

[…] Mail wasn't delivered right, just left in one big pile. People never even had the dignity of a address. Thirty-fifth Street was all. Just Thirty-fifth Street. Only ten blocks made up the colored side of that street, and at every intersection, young souls was always dropping off. Like pecans from a tree. (4-5) While Lakeland's intricate street pattern is mapped out by the city fathers who thereby confirm its reality and give it both visibility and respectability, Thirty-fifth Street is arbitrarily wiped off the map to become an uncharted dark territory, a no-man's-land. Bereft of existence and identity by officials-the dominant (male) political voice-determined to block it out of their minds, the clearly delimited street (ten blocks) is viewed as a nebulous entity, a threatening black (w)hole. As a non-space, the street implies its inhabitants' exclusion and placelessness. This secondary character-whose name rhymes with "maze"-is obviously constructed as an emblematic figure, the epitome of the impostor who endorses multiple identities so as to survive in a chaotic world. Temmy is actually "mesmerized" (143) by Mayes. "God-like in stature and form" (35) in her eyes, the slick orator is but a predator, "a massive shadow looming over the crowd" (147). In fact, streetwise Alfred Mayes bears a strong resemblance to Ellison's trickster figure Rinehart in Invisible Man or to "the snakes, the wolves, the foxes, the bears" in Ann Petry's naturalistic novel The Street (8).

Likewise, Mayes takes part in the sexual victimization of black women in a maledominated urban environment. Three female characters actually fall prey to Mayes. In the thirties, he offers the naive, young Jonetta "a big pretty room to [her]self with a lock on it"

(109) and becomes her pimp: "He was the only one I truly let inside me. Inside my room. My private room. Who I let run from corner to corner, unlocking all the doors, opening all the windows" (111). The author's use of architectural imagery, her association between Jonetta's private place and the intimacy of her body is eloquent. It signifies that, in the ghetto, the gender-based dialectic between outer and inner space, between danger and safety, is irrelevant. The door lock is an illusive barrier since men can violate women's private spaces and commodified bodies.

Later, in the seventies, Mayes enrolls Jonetta's niece Ruth-a single mother of two "shooting blues in her veins" (221)-as a member of his congregation, the New Saveds, and pays her for sexual favors from her daughter. Robbed of her innocence by Mayes's depraved mind, and forced to watch him masturbate in the dark of her room, Ruth's child Valerie "sat in a chair. She was […] sitting as though she'd been squeezed into a tiny space and asked to sit for a portrait: still and straight" (233-234). The disturbing image of the young girl, petrified and powerless, shrinking into the smallest space possible, symbolizes how black women of all generations are or may easily be caged in and objectified, confined to the role of the silent victim under male authority, thus trapped in "both the narrow space of race and the dark enclosure of sex" (Wade-Gayles 2).

Through her use of setting and characters, Dawn Turner Trice constructs Thirty-fifth Street as a confused, fragmented neighborhood, a site of violence and oppression where the protagonists have to fight against heavy odds and face painful, traumatic events. Lakeland, then, represents what the street is not: a cohesive, law-abiding community whose dreams of democracy have come true. At least that is how Lakelandites perceive themselves. As the narrative unfolds, the author builds up a reverse image of the two neighborhoods, thus revising the Manichaean opposition between suburblike Lakeland and the seedy inner city.

The Savilles live in a spacious apartment overlooking the lake: "a picture window made the lake look as though it were a beautiful painting with the sky and the water melding into similar hues" (23-24). The window is an extension into the landscape, integrating the indoor space with the picturesque outdoor space, thus giving the impression of boundless unity. Yet,

Trice uses the expanding interior as a spatial marker of division: "Our bedrooms seemed miles apart, with [Mama's] and Daddy's on the north end of our apartment and mine on the south" (24). Bourgeois life means the triumph of private space, away from the street and from others. Behind closed doors, individualities are turned inward, living in isolation within their fragments of reality. Temmy's new intimate place, her richly decorated bedroom with its "incredibly high ceiling" (23), reflects the hollowness of her new life. Feeling abandoned by her busy, hard-working father, she is deeply affected by his growing aloofness. Paradoxically, this "distant familiarity, something quite specific to Lakeland" (130), makes Temmy's mother Felicia claustophobic. "There's no breathing room here" (28), she protests, feeling stifled by the social codes of a well-mannered bourgeoisie that imposes a constant distancing, a leveling: in Lakeland, "the kingdom of the drab" (13), voices are subdued, emotions repressed so as to keep up the appearance of a perfect world.

In fact, behind its façade, beneath the surface, Lakeland reveals a more troubling reality.

Dawn Turner Trice uses the high-rise apartment building, divided up into codified spaces, as a metaphorical representation of social hierarchy. Beyond an individualistic atomization of space into private rooms and apartments, the Five forty-five building-as a collective structure-contains two coexisting worlds that tend to ignore each other, namely "top black professionals" (19) and their maids and janitors who have learned to keep their place. Like the Daltons' house-to a certain extent-in Richard Wright's Native Son, the building is partitioned along two axes, horizontal (the front and the back) and vertical (upper and lower levels), on the basis not of race but of class. As an element of Trice's dialectical construction of space, the main entrance, "the oak double door, which led to a lobby of glittering marble and crystal" (21), functions as an ostentatious representation of wealth and social status while "the back door [which] led to a cramped back elevator that all the servants used" (25)

suggests that the latter are relegated behind the scenes to a space of subordination and marginality. Besides, "most of the views opened east, out to the lake. The windows on the other side of the building [overlooking Thirty-fifth Street] were dummies. From the inside, they were plastered over, hermetically sealed" (25). The fake windows are the tangible signs of the great social divide within the black community maintained by Lakeland's nouveaux riches, who are deliberately forgetful of the ghetto.

Equally significant is the basement apartment where Valerie's brother John lives: "It was hot and humid down there, and so dark, […] the hallway […] smelled of standing water and rotten eggs" (163). The author integrates the underground motif into her Lakeland setting as a site of invisibility and stagnation. John, the head laundryman who works "like a Hebrew slave" (164) to wash the tenants' dirty linens (in private) and smooth them out, stands for the downtrodden, the black working class that contributes to the prosperity and good reputation of the place. Though functioning within the system and ensuring its durability, John or the Savilles' maid Lily and the like remain the casualties of (social) progress. Lakeland, conceived as an alternative homogeneous space, built on republican principles of freedom and equality, proves to be a place of contrasts that perpetuates oppression, segregation and exclusion.

Like the Tower of Babel, the building is the symbolic architectural expression of arrogance, diversity and fracture. Actually, the author employs biblical images to depict Lakeland as a warped and fragile collective dream. Lily, the maid and living memory of the neighborhood, explains how "Somebody filled in a swamp. Most of this land. All of Thirtyfifth Street" (138). Then, one day: Lily's flamboyant story, her mythologizing of Lakeland is saturated with apocalyptic images that reveal the true nature of the place. The domesticated land is beyond control and turns into chaos. The raging of the elements and especially the collapse into the depths of the earth signify that this grand scheme was not built on solid ground. As a neighborhood,

Lakelandites have failed to establish the necessary foundations that shape up a true community. Through Lily's urban tale, the reader is given to understand that Lakeland is an artificial place, an aggregate of social climbers who seek individual self-improvement and have made a clean sweep of their previous history.

Through her network of characters (an all-black cast) and their distinct responses to a dubious environment, the novelist addresses the key topic of urban community building, determined by black identity, gender, class and culture. She incorporates spatial imagery together with communal rituals into her narrative to express her critical views on a mainstreaming black middle class that disconnects itself from the "black folk" and has forgotten the "vernacular" traditions.

In this respect, the imposing Newhouse Country Club, symbolically set on "the highest piece of land," is a cardinal point, "something of a national monument" (173). More than a site for social gatherings, it is the representation of a collective ethos:

Once a year for the July Fourth extravaganza, the newspapers captured it in a blaze of glory as fireworks sent red, white, and blue sparkles around its crest.

[…] Every Memorial Day, legend had it, about ten gulls were gathered into a pen, dipped in blue and red food coloring, and released into the sky while the boy's choir belted out "America the Beautiful" followed by a fifteen-gun salute. ( 173)

Through triumphant and federative rituals, Lakelandites engage in the collective performance of a new urban self, in a whimsical dramatization of national pride and American identity. With much fanfare, Lakeland becomes a commemorative space that celebrates integration into the "establishment." Dawn Turner Trice also signifies, obliquely, that by adhering to the dominant cultural model, they tend to shed their African-Americanness. Paradoxically, this proud all-black community, which purposely named its streets after African American heroes and artists, is losing its color (and uniqueness) by swapping racial identity for social status. In addition, the author includes in her narrative the event of the annual ball as a visible sign of deculturation. Temmy recalls: The dance floor is a stage where the members of the clannish community can display and control their image as a group, their exclusive, self-conscious "we-ness." All moved by the same impulse, the dancers form one body. Yet, beyond the expression of symbiotic oneness, the sophisticated choreography betrays their separateness, both emotional and cultural. Following the rules of (white, middle-class) etiquette, the starchy dancers are but "mimic men" and women playing a role that allows no room for spontaneity and authenticity.

Through her concise, truncated and repetitive phrasing, the novelist skillfully manages to keep pace with the music, with the rhythmical steps of the dancers. Her minimalist phraseology reproduces their stiff and discreet moves most effectively.

As a counterpoint to her trenchant representation of the uprooted black bourgeoisie (as an empty world of cultural pretense), Dawn Turner Trice depicts Thirty-fifth Street and its inhabitants as a lively close-knit community that has managed to preserve and perpetuate African American traditions that help endure-collectively-the harsh realities of the ghetto.

Her topography of the neighborhood includes public meeting places, focal points diametrically opposed to Lakeland's Country Club, namely Jonetta's store, a hangout that makes the regulars "feel like they belong" (105), and the church. Interestingly enough, while the Newhouse Country Club testifies to Lakelandites' determination to forget a disturbing past, to put down roots and start afresh on "virgin land," Jonetta's storefront sign "O'Cala's And boy, could she dance. The entire floor rumbled with her moves. She did a showgirl kick over Mr. Chittey's little head. He hunched his shoulders and started rolling his stomach like a belly dancer as his cane slid right off his arm and his pants started to ease down his waist. She did a shimmy, rotating her shoulders, and Mr. Chittey started clapping his hands and stomping off-beat. Too cool. Miss Jonetta said, "Go, sweet feet, go!" And he kept moving. Pointing, bending, dipping east and west, then north and south. (195) The contrast with the previous scene is manifest. While the formal ball is a wellpatterned social event orchestrated by officials, the couple's sensuous, erotic moves are the free, impromptu expression of a festive mood.

Through her literary use of music and the blues motif, Trice also emphasizes "how pain and talent come together" (103). At Valerie's funeral, Jonetta's old friend Judd walks down the aisle up to the altar and strikes up a song: Judd's cathartic humming is a heartfelt testimony and a call; it is a rich metaphor of sorrow and despair, resilience and bonding. His voice, that reaches out to the responding audience, radiates as a spiritual force. The church is then filled up with Judd's contagious energy, with music and vibrations; it is breathing life. The church is a sanctuary, a communal house where the characters can ritualize their day-to-day lives so as to aleviate or exorcize their pains and unite as one community paying tribute to the deceased:

Another child had died. A child that her own mother had throwed away; that in life didn't seem to belong to nobody, suddenly, in death, belonged to everybody. That's why so many people came. Thirty-fifth Street's biggest thieves, cheats, and lowest dope dealers. (268)

Valerie's death is indeed an ultimate trial for both communities that have failed the young girl and have proved to be incapable of nurturing and protecting her: "How could I've saved that baby from so much sickness?" (4) Jonetta wonders with guilt. While on Thirty-fifth Street, the tragedy generates a sense of communal identity, solidarity and cohesion, a deepening sense of fear, mixed with disdain, prevents Lakelandites from attending the funeral-except for the Savilles. As Felicia complains bitterly, "A little girl has died, and what are people doing? They're going around putting barbed wire on the fences. Doublelocking doors" (258). Dissociating themselves further, the residents turn their backs on the street definitively and entrench themselves behind the fence so as to resist or exist as new members of the middle class.

In her review of the novel, Valerie Smith criticized Dawn Turner Trice for her dichotomous representation of the two communities, her somewhat idealized, romanticized depiction of the black underclass in parallel with her cut and dried critique of a spiritless, ossified black bourgeoisie ( 16). On this subject, the author, whom I interviewed, is quite aware that she "did go to some extremes" by representing Lakeland as a "monolith" (Duboin 118) so as to get her point across, to stigmatize class prejudices and cultural mainstreaming:

Within the confines of that ivy-lined wrought-iron fence lived this elite group of people who had been allowed to purge their minds of all those things that reminded them of what it meant to be poor and downtrodden. Once here, Lakelandites didn't look back. They surely didn't want to go back.

[…] And they vowed to put their bodies and their beliefs into this great blender and leave it there until the whitewashed folk who came out no longer resembled the pageant folk who had entered. (20)

Trice's novel clearly illustrates "the tension between race, class and cultural identity" which cultural critic Todd Boyd relates to "the assumption that Blackness is indelibly linked to a working-class ethos and singularly informed by the struggles of overcoming poverty.

Thus those who do not embrace this notion of Blackness are seen as selling out or the ultimate charge-of not being Black enough" ( 22). Boyd's critical comment about the confusion between class and ethnicity is actually well illustrated by Mr. Chittey's equivocal remark:

"Them people from across the street don't know nothing about the blues" (196). Through this ambiguous message, the character implies that black bourgeois enjoy a cozy, happy life (they never "have the blues"), and more importantly, they don't have "soul," they have lost their culture.

Addressing this difficult issue, Trice integrates the fence as a metaphor for the social and cultural divide between the black urban underclass at a dead end and upwardly mobile African Americans who ultimately, ironically, marginalize themselves further in their collective effort to conform and gain respectability. Thus, more than a physical borderline that separates the inside from the outside, the fence materializes binary oppositions between "we" and "they," unity and dissolution, ascent and downfall, good and evil. A protective buffer against the ills of Thirty-fifth Street, the fence is also symbolic of the emotional barrier

Lakelandites have erected-a fact Temmy's father will eventually realize:

"Damn it, a child has died. And now the only real thing separating us is the fence we've constructed in our minds and around our hearts. When did we forget who we are? […] All week long, we've been trying to find ways to protect ourselves from them.

[…] But we are them […]. Aren't we? We're as intricately woven as the ivy on the very fence that divides us. When did we forget that?" (261-262)

Commenting on recent African American writers, Henry Gates stressed "their capacity to express the desires and anxieties of this new middle class freely and from the inside" (40).

A member of this new generation of black writers, Dawn Turner Trice drew inspiration from personal experience and wrote a novel that focuses on class division rather than racial tensions. The author states that her narrative is not autobiographical strictly speaking (in terms of plot and action), yet she recognizes that, in some way, it mirrors her own quest: "It had more to do with my own personal journey, and me being maybe symbolic of a whole. […] Lakeland represented what had happened to me, and I found that to be not a pretty sight. To be honest, I think that my heart had hardened a little bit. There was that distancing […]" (Duboin 118). Then, the act of writing partakes of personal reassessment and self-criticism, with a focus on positionality: What do I stand up for? And, where do I belong? In her

deliberate attempt to answer these fundamental, interconnected questions, the novelist insists on the necessity to remember and acknowledge one's origins so as to be able to grow and make progress.

Only Twice closes on the Savilles' departure to California and Jonetta's return to the South after her run-down street has been condemned to make way for an extension of Lakeland: "I'll go down there for a spell and find the land I was born on and reminisce for a while.

[…] Been here too long. Too long," she confides (299). Jonetta's and her old friends' reverse migration illustrates Farah Jasmine Griffin's study on the representation of the "New South" in recent African American fiction. She observes that "the south is a haven where the failed migrant might heal from his failure" (143). Only Twice I've Wished for Heaven is indeed a novel about the fallacious promises of the modern American city that still segregates, alienates, and despoils disfranchised minorities. City building, like History, is a steady process of change and cyclical renewal, and beyond apparent contrasts, Lakeland and Thirtyfifth Street are much alike. At different times, both neighborhoods were initially viewed as utopias, potential Eldorados. In 1932, Jonetta's family moved up to Chicago, joining the mass of black southern migrants, because her father "thought 'up north' was a step away from heaven" (55). Similarly, in 1975, Temmy's father decided to move to Lakeland because he "wanted something better for the family" (258). The two places are actually described in identical terms. Jonetta recounts how, at sixteen, she first stepped into her street, back in 1932: "I came to Thirty-fifth Street that night the way the three wise men came following that star. The bright city lights called me.

[…] Seemed to me most people on Thirty-fifth Street had already found heaven, one way or another. Or at least thought they had" (50, my emphasis). Reminding us of Toni Morrison's characters in Jazz and their fascination for "the City," Jonetta is drawn by the glittering street lights. Some forty-three years later, standing outside Lakeland's gate, she also "noticed how white the pavement was behind the fence and how the bright lights made it look like diamonds had been sprinkled into the concrete" (242, my emphasis). All the metaphors and similes (lights, stars and diamonds) are so many significant details of an enticing picture. They evoke the novelty, the specialness, and the lure of the black city, the nascent urban community that has apparently so much to offer. The decline (whether material, social or moral) of both neighborhoods also leads the reader to predict that the pulling down of Thirty-fifth Street and its gentrification are somehow bound to failure.

The main characters' resulting restlessness and displacement across the city, as well as their journeys across the country, signify their permanent quest for a home. In this respect, O'Cala's "may be a hole-in-the-wall, but it ain't no gutter" (42). Together, they have managed to maintain or recreate the cohesive "village values" they grew up with in the South, and now form a tradition-bound urban community whose strong ties are built on a sense of solidarity and generosity.

Not only do Jonetta and her friends contribute to making their street somewhat bearable, but at times, they turn it into a warm and friendly environment. Actually, the grim, unsavory street exerts powerful attraction on Temmy (who strays from a comfortable neighborhood) only because of their presence as both "ancestor figures" and "cultural bearers" (Page 13,15) who keep positive values and traditions alive and pass on their heritage to younger generations. Toni Morrison once observed that "contemporary Black writers seem to view urban life as lovable only when the ancestor is there" ("City Limits" 40). Besides, she pointed out that "these ancestors are not just parents, they are sort of timeless people whose relationships to the characters are benevolent, instructive, and they provide a certain kind of wisdom" ("Rootedness" 343). Interestingly, sentenced to life imprisonment-a self-inflicted punishment: Jonetta infers "that Alfred was there, but that he didn't push her. No more than all the other nasty men had laid their hands on her. All of them" (267).

Through Valerie's poignant story, the author denounces the abdication of responsibilities on the part of adults in today's society. At the same time, she portrays politically and economically disempowered parents who end up yielding to environmental pressures, thereby furthering urban violence. The young girl's tragedy exemplifies social dislocation. It recalls us to the prejudicial absence of the "ancestor" who was not there to make sure Valerie did not "fall into the wrong hands" (55), or to give "[the] little girl a chance to enjoy a good breeze-to fix herself a dream" (5).

In a more symbolic reading, Valerie's suicide is a climactic scene, a turning-point in the initiation process Temmy undergoes. The girl's death is a most distressing rite of passage into adulthood. On that dreadful night, Temmy lost a friend, but she also lost her illusions together with her childhood-definitively.

However, the novel's final chapter offers a glimmer of hope since Temmy settles down in California and eventually starts a home and family. Her last name Saville (save/ville) is a hint at her search for a city, a safe place she can call home, and she has apparently found it.

But it will take Temmy some twenty years to overcome the aftershock of loss, face up to the past, and write down her journey across time and space, with Jonetta's help, so as to be able to look forward, not back, and be "finally, finally free" (304). Following the pattern of the black female coming-of-age story, the author suggests that healing is possible only through "the use of memory and voice" (LeSeur 197): cleavages, on the growing segmentation of (African) American life. This moving girlhood story was followed by the publication of a second novel, An Eighth of August (2000), which confirmed Trice's particular interest in such themes as black womanhood, friendship and

Food

  and Drug" (33) is a visible trace of the past. Named after its original white owner, O'Cala's is a reminder of the Great Migration-a history of black urbanization, racial tensions and displacement. Besides, within those two locales on Thirty-fifth, one secular (O'Cala's), the other sacred (the church), Trice fictionalizes cultural performances as an integral part of daily life and as the genuine expression of self, the celebration of black identity. In so doing, the author inscribes her narrative in what H. Nigel Thomas calls "a long tradition of dramatic presentation of black rituals within the Afro-American novel" (123).Symbolically, Temmy watches Miss Jonetta and Mr. Chittey dance to a record playing "Stormy Monday":

I

  told her one day she'd have to tell this thing. And it wouldn't matter if the miles stretched like canyons between us, because I would help her. One day she'd have to gather the events the way you would loose petals on a flower and piece them together again. Slowly. Into a whole story. […] It's time. So listen. (7) Through her novel's structure (with two segmented, criss-crossing narratives that juxtapose contrasted perspectives), Trice draws textual spaces and borders that recall the fragmented topography of her urban setting. Yet, Temmy and Jonetta's geographical separation and their differences will be transcended. Bridging or spiritual bonding is achieved through writing and storytelling: the author interweaves two overlapping accounts and binds their narrators together through ties of friendship, thus transmuting fragmentation into wholeness. Dawn Turner Trice's concerns echo those of prominent black female writers such as Ann Petry, Toni Morrison, and Gloria Naylor; her novel inscribes itself in the African American literary tradition. In her critique of Naylor's urban novels, The Women of Brewster Place and Linden Hills, Barbara Christian argues that "[a] single writer's juxtaposition of two Afro-American neighborhoods, different in values, separated by class distinctions, yet located in the same geographical area, is an unusual one in Afro-American literature" (107). In Only Twice I've Wished for Heaven, first-time novelist Dawn Turner Trice combines the two separate communities within one narrative and sheds light on their social and cultural

  Reminiscent of Gloria Naylor's Linden Hills, Lakeland is also "a beautiful, black wad of spit right in the white eye of America" (Linden Hills 9).At the other end of the social spectrum, but right next door, beyond the fence, lives another black community, on Thirty-fifth Street. Through Temmy's first sight of the street, Trice creates an urban environment in stark contrast to Lakeland: "The air had changed. It was damp and smelled of stale alcohol, urine, and long-standing garbage. That's what I noticed first. Grass had dulled and in most places there wasn't any, just landscaping of cracked asphalt and pockmarked concrete" (32). The author's construction of setting adds up realistic details that concur to give an overwhelming impression of decay. At once, Temmy's senses are aroused. The mixture of pungent, offensive odors, the crevices and rough surfaces

The erection of Lakeland, in place of what used to be a ghetto, and the construction of new streets "appropriately named Martin Luther King, Jr. Drive, Langston Hughes Parkway, Ida B. Wells Lane" (19) mean the collective appropriation of space. Thus, within its walls, Lakeland fosters a sense of place in conjunction with both race and class. The deliberate re-mapping and re-naming of the black city as "urban utopia" (19) indicates the determination to belong to a community united by a common ideal, namely "separate but equal." With its streets that function as sites of memory, the newly founded neighborhood claims its black heritage and enhances its collective racial identity within a multi-ethnic society. At the same time, the careful planning and building of Lakeland imply the spatial staging of a legitimate, fullfledged American citizenship: the new fancy place, built to forge a positive identity, displays individual and collective achievement, i.e. access to the upper social strata and material success. of a bleak, sterile environment that is basically mineral, all prompt-inevitably-a negative perception of space. They contribute to a somewhat conventional literary image of the ghetto common to many African American urban novels. Neglected Thirty-fifth Street is indeed representative of the black inner city on the margins, though topographically located at the center:

  […] two of the tables near the lake started sinking into the ground. Looked like the earth was just gobbling them up. […] There was a flood once, bigger than Noah's. A pipeline in the basement of the Five twenty-five building burst and water ran for forty days and forty nights. […] Well, okay, I added a little yeast to that one. But not much. And then there was the time when incinerator chutes in the Five fifteen building caught on fire. Look like that movie The Towering Inferno. God said fire would follow the Flood. Well, what really happened was they built this place too damn fast. They wanted Lakeland to shine, and in a hurry, and they didn't get stuff right."(139)(140)

"

  That night, we didn't have the benefit of the blues. […] Our steps were delicate, measured, and at times rather polite. The music moving through us in terse, refined strokes. Everybody moving the same way. Barely moving. Everybody swaying the same way. Barely swaying. Hardly touching. It was like dancing in a box. I hated it.(177)

  He closed his eyes and the melody just came. He started low, way down deep, in the part of your being that cups your secrets and disappointments and cradles them like a newborn child. Then he started to climb. […] He moved higher and higher until that big old room swole up, making way for the flood tide. His humming surrounded us. Made us feel that little girl. […] If no one knew Valerie before, through Judd, an otherwise ordinary traveler-who himself knowed her for just a few hours-they knowed her now.(271)

  Trice's novel can well be labeled as a "post-Ellison migrant novel," to borrow from Lawrence R.Rodgers's classification in Canaan Bound (181). Besides, in this coming-of-age novel, the characters' peregrinations parallel their inner journeys toward (self-)discovery.That year, Child was eleven years old, going on ninety. […] She thought nobody understood what it felt like to want to fly somewhere and be free. That's why she wandered over to Thirty-fifth Street. She was looking for a place to run to. […] Her family had just moved to this new hankty place where she felt she didn't fit in. With Valerie over there, and me on the other side of the fence, the two of us made her feel like she belonged. (6) Indeed, Jonetta plays the role of mediator in Temmy's search for identity and becomes a tutelary figure, as her repeated admonitions to the young girl show it: "And be careful crossing that street, hear? Look both ways and come straight to this store if you must. Don't you take your fanny nowhere else along Thirty-fifth Street. Understand?" (75). Akin to Mary Rambo in Invisible Man or to Miss Thompson in Paule Marshall's Brown Girl, Brownstones, Jonetta Goode (as her last name indicates) is built as a positive female character, the caring "othermother" (Collins 4) common to many black urban Bildungsromane. Her store serves as a sanctuary away from the insecurity of the street. It is a nurturing place for lost souls in need for guidance and moral support, such as Temmy, Li'l Beaver or Ruth: "Yelling, whether Bible verses or anything else, don't do no good lessin you give a child a safe place to hear it in. It's like scattering fresh seeds on hard concrete and expecting a miracle" (117).

	Trice's black city, with its distinct neighborhoods, its many nooks and corners,
	gradually becomes the scene of an initiation. Nostalgic of her former close-knit community on
	the South Side, "the only home [she]'d ever wanted to know" (11), Temmy transgresses the
	boundaries of her safe but constricting new world where she finds herself an outsider, and
	runs off to Thirty-fifth Street on several occasions to take refuge in Jonetta's store.
	With Temmy's fortuitous discovery of a breach in the surrounding railing, and later on,
	of a hidden rusty gate, the fence carries a new meaning in Trice's construction of setting. It
	becomes the ambivalent metaphor of (dis)continuity, enclosure and opening. The gate is a
	symbolic junction; its threshold, a place of passage and a narrow way that Temmy takes to
	navigate between two separate worlds and embark on a painful journey toward maturity: "I
	was determined that day to explore the rest of Thirty-fifth Street. Truth is, I didn't feel much
	like sitting still. I had on my traveling shoes […]" (141).
	Crossing borders-a challenge to (parental) authority -expands Temmy's urban
	territory and confronts her to new dangers and ordeals, as Thirty-fifth Street is the site of a
	relentless struggle for existence, for a decent life, against the many traps and pitfalls of the
	inner city. Still, Temmy's stepping into the shabby street enables her to reconnect with her
	community and regain a sense of home, thanks to both Jonetta and Valerie:

Within Trice's range of characters, and in opposition to Mayes, Jonetta represents the humane dimension of the ghetto. She and her old male friends (Mr. Chittey, Judd, Hump and Fat Daddy who meet at O'Cala's) are not lonely outcasts who face adversity and deal with the quotidian. In truth, over the years, they have learned how to survive with pride and resilience:

  Trice's rendering of the black urban experience, her colorful tableau of Thirty-fifth Street, matches Morrison's description of place and characters in contemporary African American fiction.Temmy's crossings and geographical explorations lead her to grey zones on both sides of the fence. Her young friend and confidante Valerie (who lives in Lakeland with her brother John while her mother Ruth dwells in a dilapidated tenement on Thirty-fifth Street) broadens Temmy's outlook and plays a crucial role in her initiation. She indicates her the way to the hidden gate and guides her through Lakeland's basements, through a physical and metaphorical journey backstage, into the lower depths. Valerie exposes the naive Temmy to the inner realities of Lakeland and helps her see below the surface of things. Together, they invest the subterranean world of obscurity where conventional rules of conduct are suspended. Valerie initiates her friend to the secret world of adults and their misdemeanors too shameful to mention. The basement is then the paradoxical site of darkness and vision, concealment and disclosure. In veiled terms, Valerie confides that she can "hear things" from a pipe in the cellar (165), and that she saw Mrs. Hubbard and John "doing it behind the elevator shaft" (166). But more importantly, Temmy will be led to pry into Valerie's secret.

The novel opens on a newspaper clipping, a proleptic paragraph from the Chicago Sentinel about Alfred Mayes's "murder" of Valerie in 1976 (1). The young girl's harrowing story is shrouded in mystery; gradually, through Jonetta's investigations, secrets unfold. A victim of sexual abuse and child prostitution, Valerie commits suicide at her mother's, jumping down from the twelfth floor. Temmy is a witness to the scene; so are Jonetta and Valerie's molester Mayes. Surprisingly smitten with remorse, he claims he pushed her and is


Ginisty Pascal

Guei Frederique

Girault Romain

Tosoni Julian

Olivier Jeremy

Vaxelaire Jean

Pagnol

Foulayronnes

DRYNESS LIMIT: A USEFUL PARAMETER TO ASSESS SLUDGE DEWATERING

Keywords: Dryness limit, Sludge dewatering, Flocculation, Filtration-compression cell

It is usually recognized that sludge management is a major problem in water and wastewater treatment, as it can account for up to 50% of total operating costs. The effectiveness and cost of sludge treatment and disposal operations are strongly affected by its volume. Hence, the water content (or solids concentration) of the sludge is a key parameter which can impact the different steps of the whole treatment. Consequently, thickening and dewatering are key steps in the total sludge processing train. Sludge is classically dewatered by centrifuge, filter-press, belt filter or screw filters. In every case, the process efficiency is strongly affected by sludge properties. That is why users and suppliers need a parameter to assess sludge dewaterability and a standard method to measure it. Suppliers might use this standard data to guarantee dewatering performances of their equipment.

The dryness limit is a well-known parameter used by French actors of sludge treatment. It is classically measured by a filtration-compression test until filtrate flowing stops. However, for highly compressible sludges, this condition is difficult to reach. That is why a simple mathematical model fitting compression data was used to extrapolate data for dryness limit assessment.

The objective of the research is to study the role of every operating condition listed in FD-T 97001-1 relative to sludge dryness in order to recommend values for analysts. The influence of test time, pressure, cake thickness, filter cloth, flocculation conditions, pre-thickening and storage time on the dryness limit was strongly discussed for different kinds of sludge. The results enable to establish a proper procedure to measure the dryness limit. This limit is always higher than the dryness reached with industrial devices. The deviation depends mainly on the sludge nature and the type of dewatering equipment used.

INTRODUCTION

The effectiveness and cost of sludge treatment and disposal operations are strongly affected by its volume and, thus, by water content or solids concentration. Consequently, thickening and dewatering are important steps in the total sludge processing train. They both have a serious impact on subsequent operations (storage, pumping, transportation and handling). Sorensen [START_REF] Sorensen | Filtration of activated sludge[END_REF] reports that 30-50% of annual treatment operating costs relate to the sludge dewatering stage. Sludge conditioning generally enhances the removal of water during the thickening and dewatering process. Sludge is classically dewatered by centrifuge, filter-press, belt filter or screw filters. In every case, the process efficiency is strongly affected by sludge properties, and strongly linked to organic content, state of water and rheological properties [START_REF] Ruiz | Dewatering of urban residual sludges : Filterability and hydro-textural characteristics of conditioned sludges[END_REF].

Users and suppliers need a parameter and simple methods to assess sludge dewaterability in industrial devices. Correlations were highlighted between dewatered sludge dryness and simple parameters such as Capillary succion time (CST), dry and volatile matters, pH and conductivity, specific resistance to filtration, compressibility index, Mohlman index and centrifugation index, viscosity, drainaibility index [START_REF] Salzer | Les boues des usines de depollution urbaines[END_REF]. Limit water content, corresponding to the minimum water content of the sludge cake reached after a constant pressure filtration, is another important parameter that can be useful to describe and forecast the efficiency of the filtration process or a single mechanical action.

This parameter is all the more interesting as it gives a limit to sludge dewatering performances linked to intrinsic sludge properties. Suppliers and users of dewatering equipments agree on the fact that it is a fundamental datum of sludge to give guarantees on the performances of their machines. Nevertheless, a standard method is still required. The concept of the dryness limit was defined in the old French Standard XP-T97001 Part 3 [START_REF]Essais des boues : Détermination des caractéristiques en liaison avec l'aptitude à la concentration (old French standard)[END_REF] developed in the early eighties. It represents the theoretical maximal dryness reached by filtration-compression test after an infinite operating time. Although, it does not represent the dryness reached with industrial equipment but this parameter enables to compare the dewaterability of sludges in reference conditions. Each supplier had its own correlation between the dryness limit and the dryness obtained on their equipment [START_REF] Gazbar | Assessment and improvement of performances of mechanical dewatering processes of sewage sludge[END_REF]. The problem of the XP-T97001 Standard lies on the lack of information concerning solids load, expression pressure and time which strongly affect the dryness limit. A task group was recently created in Afnor organization, in the frame of the French mirror group of CEN TC 308 "Sludges characterization" to improve the method of determination of dryness limit. It gathers French suppliers, users and universities. A first document FD-T 97001 [START_REF]Caractérisation des bouespart-1 : Détermination de la siccité limite » (French standard under progress)[END_REF] was written listing all the parameters which can influence the measurement and recommends to precise them when a dryness limit value is provided. The present work aims to impose the operating conditions for the development of a future standard.

Previous communication [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF] highlighted the role of 3 main parameters: solids load, pressure and compression time on the dryness limit of a mineral and activated sludge. This paper highlights the influence of pressure and cake thickness aiming at the reduction of the duration of limit dryness experiments. It also studies the role of other parameters: flocculation conditions, filter cloth nature, storage time, gradual increase of pressure. It compares laboratory results with sludge dryness reached with industrial devices.

MATERIALS AND METHODS

Sludge

Experiments were carried out with different kinds of sludges:.



Polyelectrolytes

Cationic polymer with different charge densities, molecular weights, physico-chemical form (powder, emulsion) and structure (linear chain, cross-linked backbone, structured) were supplied by two manufacturers: SNF FLOERGER and BASF. The amount of polymer solution used was fixed against the quantity of dry sludge (kg/T DS), according to the optimal dosage of polyelectrolyte (actives matters).

Flocculation and thickening

Sludges were flocculated before dewatering to be more representative of industrial operating conditions. Sludge flocculation experiments were carried out with a new kind of device called "bootest" developed by IFTS. This apparatus was initially used for validation of prEN 14742 standard concerning laboratory chemical conditioning procedure and already described in previous work [START_REF] Ginisty | New Laboratory Developments for sludge flocculation[END_REF]. The two flocculation tanks of 90 mm diameter each are stirred in similar conditions with measurement and control of time and speed mixing, impeller position (in function of the sludge volume). Flocs are transferred automatically from the flocculation tanks to the drainage part of the bootest. Drainage cells are equipped with filter cloth reference Si030904 supplied by Rai-Tillières (French manufacturer).

Sludge dewatering

Dewatering tests were carried out with a filtration-compression cell of 70 mm internal diameter (figure 1). A perforated disk was located at the bottom of the cylinder to support a synthetic filtering medium. Three different filter clothes, supplied by Sefar Fyltis (France) and referenced as: 05-1001-SK 025, 05-1010-SK 008 and 04-1010-K-006, were used in this study. The pressure was applied by a piston moved pneumatically. The determination of the slope of the linearized form of the model enables to assess the dryness limit (S ∞ )

Previous work [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF] showed that the model fits well compression of flocculated sludges thickened by gravity drainage.

RESULTS AND DISCUSSION

Choice of operating conditions for dryness limit determination

The dryness of biological flocculated sludge usually increases slowly with compression time, consequently, the dryness limit of the filter-cake is often reached after 24 hours of running test. Sludge dryness limit depends also strongly on solids load and consequently on the final cake thickness as illustrated in figure 2. With regards to the results reported on Figure 2, the compression time is too long to offer useful test. A part of the present work aimed to find reference conditions to achieve equivalent results with test no longer than 4 hours. Moreover, an excessively long compression time (16 h) or an excessively high pressure (30 bar) can lead to the breakage of weak flocs. A decrease of dryness limit from 72% to 50 (30 bar) or 55% (16 h) was observed for kaolin sludge flocculated with anionic polymer AN 926 SH at 2 kg/T MS.

Figure 3 compares dryness limit of activated sludge (Rouquet WWTP) for various dewatering conditions. The results show that experiment time could be decreased from 16 h to 4 h, when the sludge load was reduced from 2 to 1 kg DS/m 2 (that corresponded in our case to a final cake thickness of 5±0.5 mm). . compression time: 4 h, final cake thickness: 5±0.5 mm), in comparison to dryness achieved with industrial devices. They show a quite good agreement between the two laboratory protocols except for one activated sludge (to be checked in further work) and for mineral sludge. For the latest, the protocol might be adapted as this type of sludge behaves quite differently from biological sludges (as showed in previous work [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF]). The dryness reached with centrifuge corresponds to 0.8-0.9 of the dryness limit when the operating conditions are optimized for a dewatering purpose (that was probably not the case for Rouquet WWTP).

The ratio between laboratory and industrial data is lower for belt press (between 0.6-0.7).

Influence of other parameters

In order to consolidate the laboratory protocol, the impact of other parameters, less relevant than pressure, compression time and cake thickness was studied.

Influence of conditioning conditions

The influence of 4 main parameters was studied: nature of polymer, dose of polymer, mixing time and sludge temperature before flocculation. Results are illustrated on figures 5, 6, 7 and 8. These figures show that the most sensitive parameter is the nature of the polymer whose the cationicity and the structure influence the state of water within the cake and thus the ability to liberate water by compression. The polymer dose has a lower influence provided that sludge is properly flocculated. Overdosing increases viscosity of filtrate and can delay the release of water and cake structuration. The influence of mixing of sludge with polymer on sludge limit dryness determination is rather significant as sheared flocs are generally more difficult to dewater. It is important to control hydrodynamic parameters according to European standard prEN 14742 to obtain a repeatable flocculation. Temperature of sludge has no significant effect on the dryness limit.

Influence of storage time

Time storage of sludge before flocculation and compression was evaluated and its influence on dryness limit is illustrated figure 9. For these experiments, sludge was stored at 4°C.

Influence of filter cloth

Tests carried out with flocculated the activated sludge from Rouquet plant (protocol P1) show a difference of 2% on the dryness limit which decreased from 28 to 26% when the permeability of the filter cloth increased. Differences of the same order of magnitude were observed with the activated sludge from Moulins plant. Results have to be completed to check if this effect is significant.

Influence of pre-thickening

Comparative tests carried out on flocculated sludge and thickened flocculated sludge by gravity drainage did not point out significant differences on the final sludge dryness. Nevertheless, the application of the mathematical model is valuable only for pre-thickened sludge.

CONCLUSIONS

The concept of "dryness limit" is a useful index to assess sludge dewaterability, nevertheless, it significantly depends on solids load, expression pressure and compression time. A consensus will have to be found to select these parameters for the development of a future standard and a new simple protocol has been developed to achieve tests in a reasonable time (4 hours) to have a reference value. Obviously, sludge flocculation has also an impact on the sludge dryness and should be carried out in a repeatable way, as recommended by the standard prEN 14742.

The reference value of dryness limit should facilitate the exchanges between endusers and suppliers of dewatering machines who should give guarantees of their machine performances on the basis of this value according to their own experience.

Further work should be done to consolidate the experimental protocol and to carry out common tests with organisms involved in the project.

The authors acknowledge all the participants of the French mirror group for their contribution in this work and suppliers and end-users who provide all the sludges.

SYMBOLS

Figure 1 :

 1 Figure 1 : Filtration-compression cellFlocculated sludge thickened by gravity drainage was used for filtration-compression tests. The mass of filtrate was recorded against time over the experiments. It reached an asymptote where no filtrate was released from the cake by mechanical compression. The cake dry solids content corresponding to this asymptote was called dryness limit. It corresponds to the cake dryness obtained after an infinite operating time (as defined in FD-T 97001-1[START_REF]Essais des boues : Détermination des caractéristiques en liaison avec l'aptitude à la concentration (old French standard)[END_REF]). For compressible sludge, it is generally difficult to reach the asymptote in a reasonable test time. It is the reason why we proposed to use a simple mathematic model to extrapolate cumulative curves of filtrate mass versus time:.

Figure 2 :

 2 Figure 2: Evolution of dryness limit at 4 bar with activated sludge (Varennes WWTP) flocculated with a reticulated polymer (EM 640 BD from SNF Floerger) at 7 kg /t MS

Figure 5 :Figure 6 :Figure 7 :Figure 8 :

 5678 Figure 5: Influence of the polymer nature on dryness limit (protocol P1) with activated sludge (Rouquet WWTP) at dosage of 6 kg/T DS (only for EM 640 TRM) and 15 kg/T DS (other polymers)

Figure 9 :

 9 Figure 9 : Influence of sludge storage time before flocculation on dryness limit (protocol P2) with activated sludge (Moulins WWTP) flocculated with EM 640 BD at 7 kg/t MS Results show that tests can be carried out over the full first working week after reception.

DS : dry solids

  or dry matters S∞ : dryness limit t : compression time (s) VM : volatile matters a, b, c : constant parameters

Table 1 : Sludge characteristics after dewatering

 1

	Sludge	Floculation conditions	Dryness limit (%)	Dryness machine*
		Polymer	Dose (kg/ MS)	P1	P2	Value (%)	Ratio
	1.Activated sludge (Rouquet) EM 540 BD	15	28.5	28.8	21	0.73
	2.Activated sludge (Noyal)	EM 840 HIB	6	29.9	24.9	17	0.68/0.57
	3.Activated sludge (Varennes) EM 640 BD	7	32.7	32.8	-	-
	4.Digested sludges (Albi)	Zetag 9018	20	25.5	24.4	22	0.86 / 0.90
	5.Water supply (Apremont)	Zetag 8140	7	36	35.7	23	0.64
	6.Food (Royan)	EM 640 TBD	21	21.8	21.8	19	0.87
	7.Kaolin sludges	AN 926 SH	2	68	71.9	-	-
	*1 : centrifuge -2 : belt press -3 : no dewatering device-4 : centrifuge -5 : centrifuge -6 :
	centrifuge -7 : no data 'synthetic sludge)

FILTECH 2013 -October 22-24, 2013 -Wiesbaden -Germany


J.-B Conrardy

J Olivier

J Vaxelaire

Electro-dewatering of activated sludge: filtrate flow rate analysis

Keywords:

Dewatering of activated sludge is a difficult process. Assisting the dewatering by an electrical field improves significantly the efficiency. The purpose of this study was to analyse the kinetics of the dewatering process thanks to experiments carried out with a lab-scale pressurised electro-dewatering device. Tests were conducted under constant current density and constant voltage, respectively. Different sludge loads were considered. The kinetics of the dewatering process was monitored by calculating both, the dryness of the sludge cake and the mass flow rate of filtrate over time. It was found that only two key parameters affect significantly the mass flow rate of filtrate during the electro-dewatering process, namely the electric current intensity and the dryness of sludge cake. The dewatering kinetics of tests at constant voltage and constant current were both explained with this analysis. No influence of the sludge load was observed on the flow rate of filtrate.

INTRODUCTION

Municipal wastewater treatment leads to huge amounts of wet residues such as activated sludge. For financial reasons, the sludge needs to be dewatered prior to further disposal. Electro-kinetics effects have shown their ability to assist conventional mechanical dewatering process [START_REF] Olivier | Electrical field: A historical review of its application and contributions in wastewater sludge dewatering[END_REF]Iwata et al., 2014). The use of this combined effect is often referred as pressurized electro-osmotic dewatering (PEOD). This combined technology has been found to be cost effective compared to other drying methods [START_REF] Olivier | Electro-dewatering of anaerobically digested and activated sludges: an energy aspect analysis[END_REF]. Many operating parameters can influence the efficiency of such an electro-dewatering process. Since activated sludge is a biomaterial the dewatering behavior may vary due to the change of sludge characteristics over time. It may also differ from a sludge sample to another. Consequently, the comparison of the dewatering kinetics has to be operated only with a single sludge sample and with tests carried out on a rather short period of time (a week). The purpose of the present study was to figure out how the dewatering process behaves when varying the electric current (or voltage) and the amount of sludge in the cell (sludge load), respectively.

METHODS

The experimental set-up used for this study was previously described by [START_REF] Olivier | Electro-dewatering of wastewater sludge: Influence of the operating conditions and their interactions effects[END_REF]. It consists in a filtration/compression cell working with a pressure controlled piston moving in a cylindrical vessel (70 mm inner diameter). Two perforated disk electrodes were placed at both ends of the compression chamber. Activated sludge was directly collected from the wastewater treatment plants and flocculated with a cationic polymer prior to be thickened under gravity drainage. The dewatering kinetics was monitored by measuring the mass of filtrate over time. The dryness of the sludge cake was calculated from the cake dryness measured at the end of the process and the evolution of the mass of filtrate. Electric current and voltage were monitored as well. For all experiments the pressure was 5 bar.

RESULTS

A first series of experiments was carried out under different constant currents (200 mA, 300 mA and 400 mA) with different sludge loads (5 gDS, 10 gDS, 15 gDS). Plotting the mass flow rate of filtrate versus the sludge cake dryness turned out to be effective for explaining the dewatering kinetics of these experiments.

On figure 1, the first graph (left side) enabled to compare the flow rate of filtrate for different experiments of the first experiments series. A global decreasing trend was observed when the dryness increased (due to the dewatering process). Moreover, it appeared clearly for a given dryness that the higher the current intensity was the higher the flow rate of filtrate was. When considering two different sludge loads (5 gDS and 10 gDS), for a given current intensity, the mass flow rate of filtrate was found to be similar, at a given cake dryness, for both experiments. However it should be mentioned that this behavior led to different dewatering rate since the amount of water to be removed was different in each case. Consequently, a smaller sludge load reached faster higher dryness. At the opposite, a more important sludge load dewatered slower. A second series of experiments was carried out to compare, with a same sludge load, dewatering tests conducted under constant voltage (30 V and 40 V) and constant current (200 mA and 300 mA), respectively. During a test carried out with a constant voltage, the electric current varies over time. It starts at a moderate value, and then increases to a peak prior to decrease slowly. For this kind of test, the mass flow rate follows a similar behaviour by reaching a peak at a given dryness. The two peaks were significantly correlated for all tests carried out at constant voltage. Consequently, it is possible to assume that the flow rate was mainly correlated to the current intensity and the sludge cake dryness, respectively. Such correlations were also proposed in literature for tests conducted at constant current intensity with mineral sludge [START_REF] Iwata | Application of electroosmosis for sludge dewatering-A review[END_REF].

On figure 1, the graph on the right side shows the flow rate behaviour for the two kinds of operating conditions. For the test at 30 V, both electric and flow rate peaks were both observed when the sludge cake dryness was around 30%. The flow rate increased because the current intensity increased sharply and then decreased because of the decreasing electric current and the increasing dryness, respectively. When the electric current decreased to 250 mA, both experiments gave a similar flow rate. This study points out the possibility to explain the kinetics of tests conducted under constant voltage condition with the same kind of analysis than the one used for tests conducted under constant current.

CONCLUSION

Several conclusions can be stated from this work:

-For a given cake dryness a higher current intensity leads to a higher mass flow rate of filtrate.

-For a given current intensity, higher cake dryness leads to a lower mass flow rate of filtrate.

-When operating at constant voltage the current intensity changes and exhibits a peak. This peak is correlated with the peak observed on the mass flow rate of filtrate -The sludge loading does not affect significantly the flow rate of filtrate provided that comparisons are made at a given dryness and a constant current intensity, respectively. Consequently, a higher sludge load dewaters slower.

Figure 1 .

 1 Figure 1. Influence of cake dryness, current intensity and sludge load on mass flow rate of filtrate. Tests conducted with different constant currents and sludge loads (left side). Comparison between a constant current test and a constant voltage test (right side).


Yiping Jiang
email: jiang@recherche.enac.fr

Carl Milner
email: milner@recherche.enac.fr

Christophe Macabiau
email: macabiau@recherche.enac.fr

Code-Carrier Divergence Monitoring for GAST-F GBAS

In Ground Based Augmentation System (GBAS), non Gaussian tails are created by ionosphere when detecting a satellite payload fault with the Code Carrier Divergence (CCD) ground monitor. Ionosphere can also trigger alarms which is not distinguishable with the payload fault. Using multi-frequency observations which would be available in future supporting GBAS Approach Service Type F (GAST-F), a new CCD monitor is proposed with influence of ionosphere removed. The improved performance is shown with the empirical data and simulated scenarios. The worst case is concluded for analysis of compliance with the integirty requirement.

INTRODUCTION

The GBAS is intended to support precision approach operations standardized at the International Civil Aviation Organization (ICAO) using satellite constellations. Single frequency based GBAS Approach Service Type D (GAST-D) is developed to transfer more responsibility from the ground station to the aircraft to reach CAT II/III minima. However, the GAST-D solution whilst meeting the requirements most of the time in most locations is susceptible to ionospheric activity at times in some locations. To take advantages of the forthcoming multi-constellation and multi-frequency GNSS environment, the GAST-F has been designated to the provision of CAT III services using dual-frequency corrections which will mitigate the issues raised under GAST-D, which is under investigation within the European SESAR program (WP 15.3.7). Furthermore, the enhanced performance of the navigation system should enable lower performing aircraft to meet the CAT III requirements.

In the design of GAST-F one aspect which may be revisited to garner better performance is the design of integrity monitors for the array of threats which constitute a risk to GBAS. These threats may differ when considering new signals and constellations. This paper addresses the monitoring of the CCD on the ground caused by a satellite payload fault, which results in a lack of synchronization between the code and carrier waveform during the data demodulation and processing and after the tracking loop by GNSS receivers [START_REF] Gleason | GNSS Applications and Methods[END_REF]. The payload threat takes more arbitrary forms, which can occur on the code only or carrier only or both code and carrier. In GAST-D, multiple monitors act together to constrain the effect of this error on the ground and aircraft [START_REF] Brenner | Ranging Source Fault Detection Performance for Category III GBAS[END_REF] [START_REF] Jensen | ICAO NSP -Preliminary Ground System Monitor Validation Results[END_REF], including the CCD rate monitor [START_REF] Simili | Code-Carrier Divergence Monitoring for the GPS Local Area Augmentation System[END_REF], the excessive acceleration monitor [START_REF] Stakkeland | Estimating satellite excessive acceleration in the presence of phase scintillations[END_REF] and the carrier rate monitor. In this study, only the CCD rate monitor is of concern. On detection of such failures, the associated range source shall be removed from the valid sets or indicated [START_REF]ED-114A, Minimum Operational Performance Specification for Global Navigation Satellite Ground Based Augmentation System Ground Equipment to Support Category I Operations[END_REF].

Nominal ionosphere at low elevation angle leads to non Gaussian tails of the test metrics. This is isolated by increasing the standard deviation of the metric noise resulting in a larger threshold. However, in case of the ionosphere, large temporal gradients can still trigger false alarms in the CCD monitor. The role of the ground CCD monitor is not designed to protect against ionosphere gradient because the slowly varying ionosphere gradient is cancelled in the differential processing and fast varying gradients are detected with airborne monitoring. With GAST-D multiple frequency measurements, it is possible to remove the ionosphere with resulting advantages as follows: 1) Without the ionosphere error in the residual noise in the test metrics, the standard deviation of the metric noise does not need to account for this effect, which could potentially enable the same performance to be obtained with less allocated continuity risk. 2) The two failure types of the ionosphere and the satellite payload CCD fault, which would both trigger alarms in the CCD monitor in GAST-D, is now distinguishable and only the latter one is detected by the ground CCD monitor.

The rest of the paper is organized as follows. Starting with an introduction of GAST-D CCD monitor, the design of the new GAST-F monitor is described with the covariance matrix bounded with empirical data. Then the divergence's influence on the airborne and ground smoothing process is analyzed and the worst case differential error with CCD detection is concluded for both GAST-D and GAST-F. Lastly, the results of the Probability of Missed Detection (PMD) as a function of the divergence and the differential error are used for compliance analysis, where the worst case mapping functions are obtained for GAST-D and GAST-F.

INTEGRITY MONITORS

GAST-D CCD Monitor

In GAST-D CCD Monitor, the Code minus Carrier (CMC) single frequency observations are used. With GPS L1 pseudorange 𝜌 1 and phase measurement 𝜑 1 as an example,

𝐶𝑀𝐶 1 (𝑡) = 𝜌 1 (𝑡) -𝜑 1 (𝑡) (1)
With 𝑇 as the sample interval, the CMC rate is defined as,

𝑑𝐶𝑀𝐶 1 = 𝐶𝑀𝐶 1 (𝑡)-𝐶𝑀𝐶 1 (𝑡-𝑇) 𝑇 (2)
Thus errors common to code and carrier measurements, such as satellite and receiver clock offsets, troposphere delay, orbit and ephemeris error and etc. are eliminated. Constant errors are removed, e.g. the integer ambiguity. The difference between two epochs removes largely the slowly varying biases. The leftover errors appear in the form of rate of change of the ionosphere delay, multipath and noise. The two cascaded first order low pass filter 𝑓 is defined as,

𝐹 1 (𝑡) = (1 -𝛼)𝐹 1 (𝑡 -𝑇) + 𝛼 • 𝑑𝐶𝑀𝐶 1 (3) 𝐹 2 (𝑡) = (1 -𝛼)𝐹 2 (𝑡 -𝑇) + 𝛼 • 𝐹 1 (𝑡) (4)
where 𝑑𝐶𝑀𝐶 1 is the input and 𝐹 2 (𝑡) = 𝑓(𝑑𝐶𝑀𝐶 1 ) is the output of the filter, 𝛼 = 𝑇 𝜏 is the filter weight with 𝜏 as the time constant. Shorter time constant results in faster detection of CCD failure, and therefore less susceptible to the buildup of divergence induced filter lag errors, but the noisier test metric. In s-domain, the test metric of GAST-D is expressed as,

𝐹 2 (𝑠) = 1 (𝜏𝑠+1) 2 𝑑𝐶𝑀𝐶 1 (𝑠) = s (𝜏𝑠+1) 2 𝐶𝑀𝐶 1 (𝑠) (5)
For GAST-D, the non-centrality parameter of the test metric is the divergence rate 𝑑, and the steady state is the same which is independent of the time constant 𝜏, lim

𝑠→0 𝑠𝐹 2 (𝑠) = 𝑠 2 (𝜏𝑠+1) 2 𝑑 𝑠 2 = 𝑑 (6)
In steady state, assuming the input noise is Gauss-Markov, the resulting noise attenuation is derived below when the filter weight is small,

𝜎 𝐹2 2 ≅ 𝛼 4 𝜎 𝑑𝐶𝑀𝐶 1 2 (7)
For GAST-D, the continuity risk allocated for all monitors is 2×10 -7 per 15s and satellite, and single monitor is 1/20, which is 10 -8 per 15s and satellite [START_REF] Sarps | GBAS CAT II/III Development Baseline SARPs[END_REF]. The standard deviation of the test metric is bounded as 0.00399m/s, which is inflated to count for the fact that the ionosphere as one of the residual errors is not Gaussian [START_REF] Simili | Code-Carrier Divergence Monitoring for the GPS Local Area Augmentation System[END_REF]. With the Probability of False Alarm (PFA) as 10 -9 , the threshold is 0.0233m/s. The time constant on the ground is 30s [START_REF]WGW/Flimsy 6 -Conceptual Framework for the Proposal for GBAS to Support CAT III Operations[END_REF]. For the Airborne CCD monitoring, the standard deviation of the test metric is 0.0022m/s, the threshold is 0.0125m/s [START_REF]Minimum Operational Performance Standards for GPS Local Area Augmentation System Airborne Equipment[END_REF], and the time constant is 100s [START_REF]WGW/Flimsy 6 -Conceptual Framework for the Proposal for GBAS to Support CAT III Operations[END_REF]. This paper is only concerned with the CCD monitor on the ground.

Using GPS L1 and L5 or Galileo E1 and E5, four monitor statistics are used each with ionosphere removed, including the Divergence Free (DF) combination on L1, DF on L5, Ionosphere Free (IF) combination on CMC and IF on phase measurements,

𝐶𝑀𝐶 𝐷𝐹1 = 𝜌 1 -𝜑 1 + 2 1-γ (𝜑 1 -𝜑 5 ) (8)
𝐶𝑀𝐶 𝐷𝐹5 = 𝜌 5 -𝜑 5 - 2γ γ-1 (𝜑 1 -𝜑 5 ) (9)
𝐶𝑀𝐶 𝐼𝐹 = γ γ-1 (𝜌 1 -𝜑 1 ) - 1 γ-1 (𝜌 5 -𝜑 5 ) (10)
𝜑 𝐼𝐹 = γ γ-1 𝜑 1 - 1 γ-1 𝜑 5 (11)
where

γ = 𝑓 𝐿1 2 𝑓 𝐿5
2 . 𝑑𝐶𝑀𝐶 𝐷𝐹1 is the 𝐶𝑀𝐶 𝐷𝐹1 change rate between two adjacent epochs, which can also be expressed as a change rate of measurements 𝑑𝜌 1 , 𝑑𝜌 5 , 𝑑𝜑 1 , 𝑑𝜑 5 ,

𝑑𝐶𝑀𝐶 𝐷𝐹1 = 𝐶𝑀𝐶 𝐷𝐹1 (𝑡)-𝐶𝑀𝐶 𝐷𝐹1 (𝑡-𝑇) 𝑇 = 𝑑𝜌 1 -𝑑𝜑 1 + 2 1-γ (𝑑𝜑 1 -𝑑𝜑 5 ) (12)
Same can be derived for the change rate of the other three statistics 𝑑𝐶𝑀𝐶 𝐷𝐹5 , 𝑑𝐶𝑀𝐶 𝐼𝐹 and 𝑑𝜑 𝐼𝐹 . Since 𝑑𝜑 𝐼𝐹 is not geometry free, it needs to be compensated for satellite motion 𝑑𝑟, receiver clock drift 𝑑𝑡 𝑟𝑥 , satellite clock drift 𝑑𝑡 𝑠𝑣 and also troposphere delay for low elevation angle satellites. The phase measurements need to be checked against cycle slips for all four monitor statistics. The receiver clock is estimated by averaging the rest of the geometry-free satellites 𝑑𝜑 𝐼𝐹,𝑗 together,

𝑑𝑡 𝑟𝑥,𝑗 = 1 𝑛 ∑ (𝑑𝜑 𝐼𝐹,𝑗 -𝑑𝑟 𝑗 -𝑑𝑡 𝑠𝑣,𝑗 ) 𝑗≠𝑖 ( 13
)
where 𝑛 is the number of visible satellites excluding the one that is examined of the CCD. The compensated IF phase statistic becomes

𝑑𝜑 𝐼𝐹_𝐶 = 𝑑𝜑 𝐼𝐹,𝑖 -𝑑𝑟 𝑖 -𝑑𝑡 𝑠𝑣,𝑖 -𝑑𝑡 𝑟𝑥,𝑖 (14)
To cover arbitrary fault modes on code, carrier, L1 and L5, the only and unique solution to make the mean of each of the four statistics 𝑑𝐶𝑀𝐶 𝐷𝐹5 , 𝑑𝐶𝑀𝐶 𝐷𝐹5 , 𝑑𝐶𝑀𝐶 𝐼𝐹 , 𝑑𝜑 𝐼𝐹_𝐶 equals zero at the same time is when the mean of each measurement rate 𝑑𝜌 1 , 𝑑𝜌 5 , 𝑑𝜑 1 , 𝑑𝜑 5 is zero. With four statistics going through the same second-order filter 𝑓 as in GAST-D, the filtered statistics are 𝑓(𝑑𝐶𝑀𝐶 𝐷𝐹5 ), 𝑓(𝑑𝐶𝑀𝐶 𝐷𝐹5 ), 𝑓(𝑑𝐶𝑀𝐶 𝐼𝐹 ), 𝑓(𝑑𝜑 𝐼𝐹_𝐶 ) . Define a vector 𝑥 = [𝑓(𝑑𝐶𝑀𝐶 𝐷𝐹1 ) 𝑓(𝑑𝐶𝑀𝐶 𝐷𝐹5 ) 𝑓(𝑑𝐶𝑀𝐶 𝐼𝐹 ) 𝑓(𝑑𝜑 𝐼𝐹_𝐶 )], the quadratic form is used as the GAST-F test metric,

𝐷 𝐹 = 𝑥𝑄 -1 𝑥 𝑇 ( 15
)
where 𝑄 is the covariance matrix of vector 𝑥. Assuming there is no temporal correlation on all measurements, the covariance matrix 𝑄 is given by,

𝑄(1,1) = 𝛼 4𝑇 2 (2𝜎 𝜌1 2 + 24.9𝜎 𝜑1 2 + 12.8𝜎 𝜑5 2 ); 𝑄(2,2) = 𝛼 4𝑇 2 (2𝜎 𝜌5 2 + 41.0𝜎 𝜑1 2 + 24.9𝜎 𝜑5 2 ) 𝑄(3,3) = 𝛼 4𝑇 2 (10. 2𝜎 𝜌1 2 + 3.2𝜎 𝜌5 2 + 10.2𝜎 𝜑1 2 + 3.2𝜎 𝜑5 2 ); 𝑄(4,4) = 𝛼 4𝑇 2 (10.2𝜎 𝜑 1 2 + 3.2𝜎 𝜑 5 2 + 10.2𝜎 𝜑 1 2 𝑛 + 3.2𝜎 𝜑 5 2 𝑛 ) 𝑄(1,2) = 𝛼 4𝑇 2 (32𝜎 𝜑1 2 + 17.9𝜎 𝜑5 2 ); 𝑄(1,3) = 𝛼 4𝑇 2 (4.52𝜎 𝜌1 2 + 15.9𝜎 𝜑1 2 + 6.4𝜎 𝜑5 2 ) (16) 𝑄(1,4) = 𝛼 4𝑇 2 (-15.9𝜎 𝜑1 2 -6.4𝜎 𝜑5 2 ); 𝑄(2,3) = 𝛼 4𝑇 2 (-2.5𝜎 𝜌5 2 + 20.5𝜎 𝜑1 2 + 8.9𝜎 𝜑5 2 ) 𝑄(2,4) = 𝛼 4𝑇 2 (-20.5𝜎 𝜑1 2 -8.9𝜎 𝜑5 2 ); 𝑄(3,4) = 𝛼 4𝑇 2 (-2.26𝜎 𝜑1 2 -3.2𝜎 𝜑5 2 )
After averaging with multiple ground stations in GBAS, the covariance is further reduced as 𝑄/𝑀 with 𝑀 as the number of ground stations. Assuming the noise of 𝜌 1 , 𝜌 5 , 𝜑 1 , 𝜑 5 are Gaussian, with the Cholesky decomposition of 𝑄, the four statistics in vector 𝑥 are standardized and decorrelated, and therefore the test metric is of chi-squared distribution with 4 degrees of freedom.

ENC 2015

For GAST-F, the fault mode is defined by the location with measurements including carrier only, code only, and carrier code, and with frequency including L1 only, L5 only or both L1 and L5. Therefore, there are totally 15 fault modes: "Code L1", "Code L5", "Carrier L1", "Carrier L5", "Code L1+L5", "Carrier L1+L5", "Code+Carrier L1", "Code+Carrier L5", "Code L1, Carrier L5", "Code L5, Carrier L1", "Code L1+L5, Carrier L1", "Code L1+L5, Carrier L5", "Code L1, Carrier L1+L5", "Code L5, Carrier L1+L5" and "Code+Carrier L1+L5". Assume the divergence rate on Code L1 as 𝑑1 𝐶 , Carrier L1 as 𝑑1 𝐿 , Code L5 as 𝑑5 𝐶 , Carrier L5 as 𝑑5 𝐿 , the rate shows the same value in the steady state non-centrality parameter of the test metric as proved in [START_REF]ED-114A, Minimum Operational Performance Specification for Global Navigation Satellite Ground Based Augmentation System Ground Equipment to Support Category I Operations[END_REF]. For example, the statistic 𝑑𝐶𝑀𝐶 𝐷𝐹1 in the test metric has steady state non-centrality parameter as 𝑑1 𝐶 -𝑑1 𝐿 +

OVERBOUNDING WITH EMPIRICAL DATA

The 1Hz data collected in Pattonville with a MLA antenna is used to bound the test metric provided by Thales Electronic Systems. The elevation mask is 5 • and the filter output is only used 360s after initialization. The time constant is 30s.

There are totally 8 GPS satellites with both L1 and L5 during one day. The standard deviation of six statistics before and after filtering are shown in Table 2 where 𝜌 ̂ is the airborne carrier smoothed pseudorange, 𝑡 𝑧 is the time of application of PRC, TC is the tropospheric correction and ∆𝑡 𝑠𝑣 is the satellite clock correction from the navigation message. The characteristics of the differential error is analyzed first without detection and then together with the CCD monitor in this section. Since the filter is continuous in time, the smoothed pseudorange 𝐶(𝑠) can be expressed in Laplace domain.

𝐶(𝑠) = 1 𝜏𝑠+1 𝑐(𝑠) + 𝜏𝑠 𝜏𝑠+1 𝑝(𝑠) (21)
where 𝑐(𝑠) and 𝑝(𝑠) are the raw pseudorange and phase measurements in Laplace domain. Assume the divergence is a ramp error with the divergence rate in code only as 𝑑 𝐶 , phase only as 𝑑 𝐿 and both code and phase as 𝑑 𝐶 -𝑑 𝐿 , the smoothed range error only has steady state 𝑑 𝐿 𝜏 when divergence is in phase only. This is derived by

lim 𝑠→0 𝑠𝐶(𝑠) = lim 𝑠→0 ( s 𝜏𝑠+1 • 𝑑 𝐶 𝑠 2 + 𝜏𝑠 2 𝜏𝑠+1 • 𝑑 𝐿 𝑠 2 ) ( 22
)
The rate of the smoothed range error has steady state of 𝑑 𝐶 , 0 and 𝑑 𝐶 for code only, phase only and both code and phase respectively, which is derived by,

lim 𝑠→0 𝑠[𝑠𝐶(𝑠) -𝐶(0)] = lim 𝑠→0 ( 𝑠 2 𝜏𝑠+1 • 𝑑 𝐶 𝑠 2 + 𝜏𝑠 3 𝜏𝑠+1 • 𝑑 𝐿 𝑠 2 ) (23)
Therefore, the steady state of the smoothed error is related with time constant 𝜏 when divergence is in phase only. With differencing the smoothed pseudorange from the ground and airborne filters, the differential range is subsequently ENC 2015 influenced by the divergence magnitude, the fault onset time 𝑡 𝑓 , the ground filter initializing time 𝑡 𝑔 , the airborne filter initializing time 𝑡 𝑎 and the time delay from initialization of the airborne filter to incorporation of the measurement in position solution 𝑡 𝑑𝑒𝑙𝑎𝑦 .

The GAST-D results of the 30s smoothed error and the 30s differential error 𝐸 𝑟 without detection are shown in Fig. 5 with the worst case when the ground filter is initialized 360s before fault onset, and the airborne filter is initialized at the same time with the fault onset. For GAST-F, there are two smoothing filter for L1 measurements and L5 measurements respectively. The airborne smoothing filter can have variant time constant or invariant time constant. For the variant time constant, with time 𝑡 from filter initialization for duration of 𝜏, [0~𝜏], the time constant is variant as 𝑡. After this, the time constant is also constant as 𝜏, which is the same as the ground time constant. In this simulation, the random error is neglected, the divergence magnitude is 0.01m/s for "Code" only, -0.01m/s for "Carrier" only and both 0.01m/s and -0.01m/s for "Code-Carrier", and 𝑇 = 0.5𝑠. In Fig. 5, when both air and ground filter are stabilized, the differential error is zero. During the transient state, all "Invariant" results are zero, and "Code Variant" is the same as "Carrier Variant", which are half the magnitude of "Code-Carrier Variant". This can be explained by the expanded equation of the differential smoothed error. A key parameter is the delay to incorporation in airborne solution 𝑡 𝑑𝑒𝑙𝑎𝑦 . The maximum differential range error with "Carrier Variant" as a function of 𝑡 𝑑𝑒𝑙𝑎𝑦 and 𝑡 𝑎 -𝑡 𝑓 is shown below. With the GAST-D CCD monitor and threshold set as 0.0233m/s, the detected measurements are removed out of the ground and airborne smoothing filter. With delay to incorporation as 50s, the value of which is proposed to be standardized, the maximum differential error as a function of the divergence rate magnitude and the airborne initialization relative to fault onset are in Table 3. In Fig. 6, the GAST-F differential error have similar characteristics with the GAST-D results, where "Code" is the same as "Carrier", which are half the magnitude of "Code-Carrier".All failures happened on L1 obviously does not have effect on the L5 differential error. For the differential error with detection, the GAST-F CCD monitor is not able to distinguish if there is failure on L1 or L5, so the measurements are removed out of the ground and airborne L1 and L5 smoothing filter when there is any failure on L1 or L5. With bounded covariance matrix and PFA set as 10 -9 , the threshold is 47.8795 (m/s) 2 . The worst case differential error with detection as a function of the divergence rate magnitude and the airborne initialization relative to fault onset is listed in Table 4 with L5 as an example,

THE PMD AS A FUNCTION OF THE DIFFERENTIAL ERROR

First, the projection from the divergence domain 𝑑 and the non-centrality parameter 𝛿 in the test metric domain needs to be examined. The ratio of 𝑑 and 𝛿 is always unit in GAST-D no matter if the divergence is code only, carrier only or both code and carrier. However, with the new non-linear monitor in GAST-F, this ratio not constant as shown in Fig. 7 for all fault modes with divergence in code the same as the x-axis 𝑑 and divergence in carrier as -𝑑, and the same value is assumed on L1 and L5. The GAST-D is not shown in Fig. 7, whose ratio is much smaller than all GAST-F ratios. As shown in Fig. 7, with the same divergence magnitude, some fault modes would produce bigger non-centrality parameter, making it easier to detect the failure, including "Code-Carrier L1 Code L5", "Carrier L1 Code L5", "Code-Carrier L1" and "Carrier L1". Consequently, this ratio influences the PMD performance as a function of the divergence magnitude with given threshold. As shown in Fig. 8, the modes with bigger ratios in Fig. 7 have better PMD performance. The PMD required region is defined as a function of the differential error illustrated by the blue line in Fig. 9 and Fig. 10 [8]. Therefore, the mapping function defined as the ratio of the non-centrality parameter of the test metric 𝛿 and the differential error 𝐸𝑟 with unit 1/s needs to be studied. The PMD as a function of the test metric can be expressed as PMD as a function of 𝐸𝑟 with a given mapping function. For GAST-D in Fig. 9, the green line is the worst case that is able to fulfil the requirement with normal distribution, which is derived by assuming that the mapping function is 0.0276 (1/s) with PFA as 10 -9 and standard deviation of the test metric 0.00399m/s. For the GAST-F monitor in Fig. 10, the green line is also the worst case that is able to meet PMD requirements, which is derived by multiplying the non-centrality parameter by 56.6294. If the mapping function is bigger than 0.0276 (1/s) in GAST-D, which is defined as the critical mapping function, the PMD requirement can be satisfied. Similarly, the 56.6294 (1/s 2 ) is the critical mapping function in GAST-F. The worst case mapping function as a function of the divergence rate and the airborne initialization time vs. fault onset with delay to incorporation as 50s are shown in Table 5 and Table 6.

Fig. 1 .Fig. 3 .

 13 Fig. 1. GAST-D L1 CCD Monitor Fig. 2. L5 CCD MonitorWith the threshold set as 0.023m/s in GAST-D, there is a false alarm triggered in both Fig.1and Fig.2with SV27 due to ionosphere delay at low elevation angle, which can be avoided with the new DF and IF combinations. Two of the four statistics in the new GAST-F test metric are shown in Fig.3and Fig.4as the DF on L1 and L5.

Fig. 5 .

 5 Fig. 5. GAST-D Differential Error Fig. 6. GAST-F L5 Differential Error with Variant Filter

Fig. 7 .

 7 Fig. 7. GAST-F Non-centrality Parameter as a function of 𝑑 Fig. 8. GAST-D and GAST-F PMD as a function of 𝑑

Fig. 9 .

 9 Fig. 9. GAST-D PMD Compliance Fig. 10. GAST-F PMD Compliance

  magnitude (m/s) non-centrality parameter of the chi-2 test metric (m/s) carrier l1 code-carrier L5 code L1 code-carrier L5 code-carrier L1 carrier L5 code-carrier L1 code L5 code-carrier L1-L5 GAST-

Table 2 .

 2 with 𝑑𝐶𝑀𝐶 5 as the CMC rate on L5, Standard Deviation of 6 Statistics before and after Filtering ), the results after filtering should be 1/120 of the results before filtering. But the results in practice does not exactly coincide with this conclusion, which is caused by the discrepancy with the assumption of pure Gaussian-Markov. The filter reduced fast varying error, while the slow varying part is relatively kept. Since the leftover low frequency part causes stronger correlation between L1 and L5, such as the ionosphere error in f(𝑑𝐶𝑀𝐶 1 ) and f(𝑑𝐶𝑀𝐶 5 ), the correlation is not negligible. The bounded covariance of the test metric with empirical data is,

	Before	𝑑𝐶𝑀𝐶 1	𝑑𝐶𝑀𝐶 5	𝑑𝐶𝑀𝐶 𝐷𝐹1	𝑑𝐶𝑀𝐶 𝐷𝐹5	𝑑𝐶𝑀𝐶 𝐼𝐹	𝑑𝜑 𝐼𝐹_𝐶
	(m)	0.1451	0.0456	0.1451	0.0458	0.1451	0.0163
	After	f(𝑑𝐶𝑀𝐶 1 ) f(𝑑𝐶𝑀𝐶 5 ) f(𝑑𝐶𝑀𝐶 𝐷𝐹1 ) f(𝑑𝐶𝑀𝐶 𝐷𝐹5 ) 𝑓(𝑑𝐶𝑀𝐶 𝐼𝐹 ) 𝑓(𝑑𝜑 𝐼𝐹_𝐶 )
	(m)	0.0032	0.0055	0.0012	0.0012	0.0031	0.00085
	With (7𝑄 = [	0.1484 0.0001 0.1356 0.3353 -0.1709 0.9735		] × 10 -5	(18)
				0.0003 0.0004	0	0.0724
	4. THE WORST DIFFERENTIAL ERROR

In GBAS, both the ground station and airborne user smooth the raw pseudoranges with a Hatch filter,

𝜌 ̂(𝑡) = 𝛼𝜌(𝑡) + (1 -𝛼)[𝜌 ̂(𝑡 -𝑇) + 𝜑(𝑡) -𝜑(𝑡 -𝑇)]

(19)

where 𝜌 ̂ is the smoothed pseudorange, 𝜌 is the raw pseudorange, 𝜑 is the raw phase measurement,

𝛼 𝑠 = 𝑇 𝜏 𝑠

is the smoothing filter weight and 𝜏 𝑠 is the time constant. There is an introduced 30s smoothed pseudorange in GAST-D in addition to the original 100s time constant. Besides monitoring the GNSS signals, the GBAS ground station transmits differential corrections via a VHF Data Broadcast (VDB) every 0.5s. Among the broadcast information, pseudorange corrections (PRC) and range rate correction (RRC) are computed with ground smoothed pseudoranges, which are used by airborne to calculate the differential pseudorange 𝜌 𝑐 , 𝜌 𝑐 = 𝜌 ̂+ 𝑃𝑅𝐶 + 𝑅𝑅𝐶(𝑡 -𝑡 𝑧 ) + 𝑇𝐶 + 𝑐∆𝑡 𝑠𝑣 (20)

Table 3

 3 GAST-D Maximum Differential Error with 𝑡 𝑑𝑒𝑙𝑎𝑦 =50s

	Failure	Carrier	Carrier				Code+Carrier
	Source	Variant	Invariant				Invariant
	Max(Er)(m) 0.1745	0.1142	0.1763	0.1142	0.1524	0.111
	Div.(m/s)	0.04	0.04	0.04	0.04	0.02	0.02
	𝑡 𝑎 -𝑡 𝑓 (s)	35	35	35	35	-150	-150

Table 4

 4 GAST-F L5 Maximum Differential Error with 𝑡 𝑑𝑒𝑙𝑎𝑦 =50s

		0.1										0.1
																		code-carrier	L1	code	L5
		0.09										0.09
																		code-carrier	L5	code	L1
		0.07 0.08					Air Code Variant Air Code Invariant Air Carrier Variant			(m) error	0.08 0.07						code-carrier code-carrier code-carrier	L5 L1-L5 carrier L1 carrier	L1 L5
	Differential Pseudorange Error(m)	0.03 0.04 0.05 0.06					Air Carrier Invariant Air Code-Carrier Variant Air Code-Carrier Invariant			pseudorange corrected	0.05 0.06 0.03 0.04						code-carrier code L5 carrier L5 code L1 carrier carrier L1 L5 code L1 L5 carrier L5 code L5	L1 L5
											L5							carrier	L1
												0.02						code	L1
		0.02
																		code-carrier	L1
												0.01
		0.01
												0
		700 0	800	900	1000	1100	1200	1300	1400	1500		700	800	900	1000	1100	1200	1300	1400	1500
						Time(0.5s)									time	(per	0.5s)
							Failure		Code L5	Carrier L5	Code+Carrier
							Source		Variant			Variant		L5, Variant
						Max(Er)(m)		0.0625		7.153×10 -6	2.302×10 -4

Table 5 .

 5 GAST-D Minimum Mapping Function with 𝑡 𝑑𝑒𝑙𝑎𝑦 =50s

	Failure	Carrier	Carrier
	Source	Variant	Invariant

2.2 GAST-F CCD MonitorThe ionospheric delay is eliminated by using multiple frequency measurements in GAST-F. As the starting point, the CCD caused by the payload fault is assumed to have an arbitrary form in GAST-F. If the satellite fault is originated from the oscillator only, the divergence rate magnitudes between two difference frequencies should be equal with the ratio of two frequencies. But if this is valid, the divergence in code and carrier measurements should also have a similar ratio in the single frequency GAST-D monitor. Since this was not assumed, the assumption of the ratio of two frequencies is also not accepted and arbitrary divergence rates are assumed.

ACKNOWLEDGMENTS

The authors would like to thank Thales Electronic Systems for the provision of data and partners of the SESAR WP 15.3.7. We would also like to thank Frieder Beck and Morten Stakkelan for their help and advices. This study is based on work supported by SESAR Joint Undertaking, created by ENAC, DSNA and Thales Electronic Systems within the frame of the SESAR Programme co-financed by the EU and EUROCONTROL. Any opinions, findings, or conclusions expressed in this study are those of the authors and do not necessarily reflect those of the SESAR Joint Undertaking.

Code Variant Code Invariant Code+Carrier Variant code L1 carrier L1 code L5 carrier L5 code-carrier L1 code L1-L5 code L1 carrier L5 carrier L1 code L5 carrier L1-L5 code-carrier L5 carrier l1 code-carrier L5 code L1 code-carrier L5 code-carrier L1 carrier L5 code-carrier L1 code L5 code-carrier L1-L5 Code Variant Code Invariant

With all results bigger than the critical mapping function, the PMD compliance of GAST-D and GAST-F can be concluded. Also, comparing Table 3 and Table 5, the worst case differential range error does not happen at the same condition with the worst case mapping function, and the latter one should be defined as the real worst case in context of PMD compliance.

CONCLUSIONS

A new GAST-F CCD monitor is designed and demonstrated under the original GAST-D framework. The advantages of removing the ionosphere is shown with empirical data. With only eight satellites transmitting on the L5 frequency, the application of IF carrier combinations has difficulty to obtain enough satellites to remove the receiver clock with high precision, and therefore reducing availability. But this problem will be relieved as more L5 satellites are available.