Interview: Yrsa Sigurdardottir, writer

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'The problem with being a crime writer in Iceland," says Yrsa Sigurdardottir, "is that there's not that much crime there to write about. Icelandic murders, as well as being rare, tend to have a depressing stupidity about them.

• Yrsa Sigurdardottir, by day she builds dams, by night she's Iceland's crime queen

"It's always been like that. In one of the best of the Icelandic sagas, Egill is forced to explain to his father why, aged four, he has just killed a man. He says he couldn't help himself; the man was just so well positioned for a bludgeoning. That was in 914. Things haven't changed much."

Don't feel too sorry for her. Iceland's only female crime novelist is doing well out of it all the same, her career helped by a series of coincidences. First of all, there's the Stieg Larsson effect: Nordic crime has never been more popular, and more of us are prepared to take a chance on a novel set in a faraway northern land about which they know nothing. Then there's the subject of her latest book: erupting Icelandic volcanoes. You can't get much more up-to-the-minute than that.

I'm in Iceland to find out more about her. I've only got a day, and she's only got an afternoon. Because Yrsa Sigurdardottir doesn't live by writing alone: her time isn't all her own. Oh no: she also builds dams. And not just any damn dams. For her last major project she was technical manager on the Karahnjukar dam in remote east Iceland, the biggest of its kind in Europe and the largest construction project in Iceland's history.

She picks me up at my Reykjavik hotel and we drive off in search of Thora Godmunsdottir, her fictional hero. This is, of course, a ridiculous notion, yet I've always been interested in the bits of the real world that writers put into fiction and how accurately they depict it when they do.

First of all, we go to the Pearl. It's on the highest bit of land near the city centre and consists of five massive tanks holding geothermally heated water (and one containing a Viking exhibition) with an enormous exhibition space and domed restaurant in the middle. Outside, there's a man-made geyser which goes off every day at one o'clock: we watch it from the viewing platform four storeys up, and when it's subsided Yrsa points out a small beach about a mile away. "That," she says, "is where we heat the ocean."

Of course we go there straight away, because I've never seen a heated ocean before, and as we drive, Sigurdardottir tells me that it's not as wasteful as one might think, that only after the heat has been used for housing, under-pavement piping and all the other things you might want to do if you have free energy on tap does the spare heat go to warm up the ocean.

She's built a geothermal plant herself, of course. She knows about these things.

"In engineering you have somebody's problem and you have to fix it. In writing, the difference is that instead of solving somebody else's problems, I get to make up my own and solve them.

"Writing's much easier than life because you control everything and everybody, but the challenge is to do that and make the events plausible. And the third element is to bring the characters to life, which is what stops it being a two-dimensional jigsaw."

In Sigurdardottir's case, this means coming home, switching on the computer, clearing her mind of water flow rates and vertical penstocks and potential megawattage and concentrating instead on Thora, her lawyer protagonist.

(And yes, I've already pointed out that in Britain the notion that a sassy young heroine should be called Thora requires a pretty large suspension of disbelief: but it probably doesn't in the other 29 languages into which her books are translated.)

"The two things – writing and my work – are so different that it doesn't feel like a long working day," she says. "Besides, when I was working on the hydro project, there wasn't anything else to do."

But having a lawyer as her protagonist means the murders in a Sigurdardottir novel require a few elements lacking in the 1.3 murders committed on average each year in Iceland. Whereas those cases usually involve nothing more than a drunken fight between two men, her incredibly tightly sprung plots will depend on the resolution of wills, on property claims.

Murders with motives. A seemingly innocuous case in the present will invariably open up into an altogether more horrendous one in the past. But at least the reasons for the killing will be satisfactorily complex, rather than a knife in the hand and a sudden rush of blood to the head.

After the heated ocean (OK, there's only about 300 yards of it, and the temperature goes from Caribbean to Arctic 50 yards out) we head back to the city centre. Reykjavik doesn't have the feel of a capital city, no more than Inverness does: it's an amiable architectural jumble with no clearly discernible central hub. That applies even in the property market: only recently have city centre flats risen in price faster than most of the suburbs.

The square outside the parliament (think tiny Victorian municipal hall, nothing like our own dear white elephant) may have access roads as narrow as a McDonald's drive-through, but it's the nearest Reykjavik comes to a city centre, so that's where we head next.

There are half a dozen protesters across the road from the parliament, where toys are strung on a length of rope between the lampposts, reminders to the politicians across the road that after the financial crash of 2008 – the kreppa, as it's universally called – these are the kind of things parents can no longer afford to give their children.

"What you've got to remember about Iceland," says Sigurdardottir, "is that it's pretty much a small, face-to-face society. That's why I don't do more than one interview a year in the Icelandic media – people would get bored – and that's the whole point of our surnames being the way they are. So because my husband's called Olaf, my son's surname is Olafson and my daughter's is Olafsdottir. It's great: you meet a stranger and they won't be able to tell anything about you from your name."

Historically, Iceland was an egalitarian society. In a 1703 census, 99 per cent of the people put themselves down as either farmers or farmworkers, and of the remaining one per cent, 194 were ministers and 150 were maids. A poor country until it discovered how to harness its natural resources in the 20th century, and until the Second World War highlighted its strategic importance, pre-kreppa Iceland seemed a relatively classless one too.

That's how Sigurdardottir – who was born in 1963 – remembers it, anyway. Pharmacists were rich (not doctors or dentists) but that was about it. No particular Reykjavik suburb was more sought-after than anywhere else. "And now, with these bankers – there's just 20 people, everyone knows who they are – everything's ruined. Robbing charities, for God's sake. And Britain using these laws against us like we're terrorists.

"You see, that used to be the thing about being Icelandic. We don't have an army, so we've never done anything to any other nation. But we really care about how our country is perceived abroad. I remember a couple of years ago there was an item on the news about Leonard Cohen arriving to play a concert in Iceland.

"And there's this interviewer asking him, as he walks down the steps of the plane, 'How do you like Iceland, Mr Cohen?' Well, that's us all over. I don't get rung up by the newspapers and asked to comment on real-life crime, but if I've been invited to a foreign book festival, for example, or if my books are to be translated into another language, they'll always want to use that. They'll be proud.

"We thought we weren't a corrupt country, but it turns out that we were about the most corrupt one in Europe. Because we're so tiny, you can't find anybody who's not involved so we've had to bring in someone from Sweden to investigate the banking collapse. Because they weren't fools, these bankers: they brought all kinds of people onto the boards, like it was a way of getting themselves immunity."

So witheringly does Sigurdarddottir talk about the bankers who shredded Iceland's reputation that it's easy to imagine her writing a novel in which one is bumped off. But she's not having any of it. "I'm just so upset by it all that I thought I'd better not write anything about them."

We head for the suburb of Seltjarnarnes, where Thora lives as well as Sigurdardottir. Thanks to "these bankers" who started paying over the odds for properties there, it's now seen as a Reykjavik's most exclusive suburb. Again, that social stratification only came in recently: when Sigurdardottir was growing up there in the 1960s it didn't have any such image.

Sigurdardottir lives on a cul-de-sac that ends with the sea. It's'a hot day, definite shirtsleeves weather (in Iceland: who'd have thought?), and I pause to take in the view. A windsurfer's board, attached to a buoy, drifts lazily from the shore in front of us.

In the distance, to the south-west is the international airport at Keflavik, where Olaf works as an assistant hotel manager; head south at that headland and there's no land until Antarctica; to the south-east, 100 miles away, lies the volcano that's done more to put people off flying than anything else this year. You could still see the top of its plume of ash and steam for most of April and May.

The nearby Eldfell volcano is just across the water on the Westmann Islands. In January 1973, it exploded, covering the small town of Heimay with ash and lava. Amazingly, nobody died that night, and the site is now open as a tourist attraction "the Pompeii of the North".

"In my new story,"?says Sigurdardottir, "Thora's client is a man who owns a house in which, when they excavate the basement, they find four bodies and a head mummified by the heat. As he was opposed to the dig in the first place, he immediately becomes the prime suspect.

"But four people going missing in Iceland for over 30 years? In Iceland, nobody ever goes missing. I mean, they might, but somebody always knows where they are. It's like I said at the start, we get the wrong kind of crimes here."

Ashes to Dust by Yrsa Sigurdardottir is published this week by Hodder and Stoughton, priced 12.99.