Claudia Llosa’s “Aloft” is set in the frigid north of Canada, and despite all the dramatics, mysticism and quasi-poetic metaphors it trades in, it’s likely to leave you cold—as well as bewildered. Despite the title, the ambitious but muddled picture never takes off.

Jumping back and forth in time, the story begins twenty-some years in the past, as Nana (Jennifer Connelly, who works in some sort of stockyard (we see her helping a pig give birth), brings her two children, Ivan (Zen McGrath) and Gully (Winta McGrath), to a remote site where a faith healer known as The Architect (William Shimell) has constructed a tunnel-like edifice of tree limbs. Holding a sort of lottery among the desperate families that have brought their ill children to see him, the healer selects one boy to enter the tunnel with him for a ritual laying on of hands—not, unhappily, Gully, whom we later learn has an inoperable brain tumor. Unfortunately, Ivan’s pet falcon—we’ll be told that he was instructed in falconry by his grandfather Peter McRobbie)—disrupts the ceremony by flying into The Architect’s construction and wreaking havoc there, leading one disgruntled father to kill the bird.

But the ritual had in fact been successful—not, however, because The Architect had laid hands on the boy’s eyes, but because Nana had done s while trying to protect him from the falcon. She, it appears, actually possesses healing powers, and will be pressured to use them. Curiously, it seems she never tries to cure Gully; instead, working with The Architect, she goes out into the woods to construct weird tree-swings as adjuncts to her efforts. (These wooden structures, it must be admitted, have a strange beauty to them, especially when set against the perpetually icy backgrounds.) It’s during one of these outings that a family tragedy strikes that will take her and Ivan onto different paths in their later lives.

Before that’s revealed, however, we’ve been introduced to the present-day Ivan (Cillian Murphy), a reclusive soul who has a wife (Oona Chaplin) and young son, but apparently spends most of his time in a shed out back where he breeds falcons. There he’s visited by Jannia (Melanie Laurent), a documentarian who claims to be working on a film about falconry but, as Ivan quickly divines, is actually seeking information about Nana’s whereabouts. Put off by this, he orders her to leave, but quickly changes him mind and demands to accompany her to the Arctic regions, where she’s discovered that Nana is plying her trade as a healer. During the journey Ivan and Jannia grow close, but on arriving at Nana’s remote outpost it becomes clear that they both have very different agendas.

It’s difficult to make out what Llosa is aiming for with this strange fable, which continually shifts from past to present to construct each part of the narrative like two puzzles being slowly assembled. The motivation of characters is often unclear, and their actions are frequently bizarre. Given that, it’s no surprise that the performances come across as forced and unfinished. Connelly evinces a generalized intensity, but is defeated by Nana’s opacity, while Murphy broods his way through the entire film; and while the kids are more open and natural, Laurent is defeated by the fact that Jannia is a painfully underdeveloped figure. The falconry motif is apparently meant to have some deep metaphorical meaning, but it’s hard to discern what it might be, though the birds themselves are impressive.

The picture has some visual power, too. The cold ambience, with the sound mix reflecting the crunching of snow and ice underfoot, is convincingly caught in Nicolas Bolduc’s luminous widescreen cinematography. One image of bodies floating beneath the surface of an ice-covered lake is particularly striking, with some of the same horrible beauty of the famous shot that Charles Laughton fashioned of Willa Harper’s submerged corpse in “The Night of the Hunter.” Another scene, in which the ice covering a frozen lake crackles and pops as the older Ivan tries to cross it, is genuinely scary. The Architect’s constructions also show considerable artistry. For the most part, however, the Llosa and her crew are satisfied with a gritty, cinema vérité look that comes across as pedestrian.

There may be some who will discern profundities in “Aloft” that will elude the vast majority of viewers. Most, however, will simply find it a largely incomprehensible story told in a painfully lugubrious, structurally fractured fashion.