As polar ice melts, deserts encroach and floodwaters rise, the presence or absence of water increasingly compels the attention of the warming planet. Artists treat it in their different ways, but few are more committed to the subject than the New Yorker Roni Horn. As she says, when we talk about water we are talking about ourselves, and she poses the challenging question: “When you look at your reflection in water, do you recognise the water in you?”

Iceland is a marvellous place in which to think about water. In this unyielding, mountainous land, with its great icecaps and 24 glaciers (now slowly melting) people must live largely from the sea. There is a lot of snow, sleet and rain here, but not all the hydrology is cold. Water boils up continually from springs and geysers heated deep underground. These make power, as well as delicious natural outdoor swimming pools, and meanwhile pure Icelandic drinking water is among the economy’s fastest-growing exports.

Horn went to Iceland two decades ago as an art student and was possessed by the grand, lonely, weather-nuanced landscape. In the years between she became a “permanent tourist” there, and now her dedication has borne fruit at the western settlement of Stikkishólmur, a gentle fishing harbour surrounded by block-like clapboard houses. Here, with the help of the British art-funding agency Artangel, she took over the former hilltop library, whose bay window commands the town and ocean like a coastguard’s look-out, and turned it into an art installation – Vatnasafn, or Library of Water. This will double as a community centre, and double again as the living quarters of a writer-in-residence.

The work is 24 glass columns scattered around the room where the book stacks once were, each filled floor-to-ceiling with water retrieved from one of Iceland’s disappearing glaciers. The obvious conceptual element to this – an “archive” for a disappearing natural phenomenon – combines with pleasing visual effects as the columns reverse, bend and compress the light seen through them. There is nothing else in the space but a spongy rubber floor in which words are inlayed in fridge-magnet lettering. They are the English or Icelandic adjectives we use to describe weather: gloomy, balmy, torrid; köld, snarpur, slarkfært.

To mark this opening, the Reykjavík Art Museum has given Horn a solo exhibition of mostly recent work, some of the best also being water-related. Of special interest to any Londoner is Still Water (The River Thames, For Example) – 15 beautiful large-scale photographs of the surface of the river, which acquires the appearance of rock-like solidity in a riff on Horn’s belief that “it is a troubling thing to stop water in its movement”. Some will be intrigued by the tiny note-numbers scattered across the surface, keys to Horn’s pensées about water printed along the lower margins. But these “reflections”, though entertaining, are mainly, for me, a distraction.

Another arresting work is You Are the Weather, 100 colour and monochrome C-prints arranged at eye-level in an unbroken line around the wall of an otherwise empty white room. They are headshots of the same young woman immersed to the neck in the hot water of various Icelandic springs, her fair hair wet, her enigmatic china-blue eyes surrounding you and outnumbering your gaze a hundred to one.

Horn will never be a crowd-pleaser, partly because she does not want to be, and partly because the work often seems over-determined, literary and rather severe. On the other hand, hers is a seriousness to be reckoned with, at a time when there is not too much to laugh about in the state of the environment we all share.

‘Roni Horn’, Reykjavík Art Museum, until August 19, tel +354 590 1200. Vatnasafn/Library of Water, Stikkishólmur,

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