Meteorology does not equal destiny, does it?

“We’re not going to talk about the weather,” Anna Ternheim said. The Swedish singer-songwriter was sitting at a table in the back of Yaffa Café, near St. Mark’s Place, enjoying a late lunch on a recent afternoon. As a brand-new arrival to New York, where she has been playing a string of low-key concerts, Ms. Ternheim was fielding questions about national identity and the emotional temperature of her songs.

The gloomy Swede, starved for sunlight, is a cliché, she insisted. It takes resolve not to mention that the cover photograph for Ms. Ternheim’s American debut, “Halfway to Five Points” (Decca), features the singer-songwriter with her head bowed, standing beneath a sky of blackening clouds. But we’ve only just met.

“Some part of it is true, of course,” she said. “I don’t know why, but all Swedish folk music has that melancholy to it. Also, there’s a lot of melody to Swedish pop music while not as much rhythm. There’s definitely a color to the Nordic music. We don’t surprise people. It’s like, I’m the Swedish singer-songwriter girl from Sweden in the north, singing sad melancholic songs!”

Ms. Ternheim, who is slender, blond, and turns 30 this month, laughed a bit. Then she flipped the topic around. “Really, people are writing about the same things and have the same concerns always: love, life. There are so many unique experiences and it’s those different layers you try to find. And those sensations you get listening to music, those emotions, you can share with people, and then maybe it’s not as predictable all the time. If you somehow manage a new way to say something.”

That’s the performer’s task at the moment, as she tours to promote her album after a meteoric career back home, where she won the Grammy for Best New Artist and has joined a small new wave of songwriters that has risen in the past five years. Ms. Ternheim will perform Wednesday at Joe’s Pub and Thursday at the Bowery Ballroom with two other women, Sarah Assbring (aka El Perro Del Mar) and Lykke Li. The singer has gotten reacquainted with her backlog of tunes, which she performs solo on acoustic guitar or a keyboard, without her band.

The stripped-down shows expose the emotion coursing through Ms. Ternheim’s songs in a more raw and vulnerable way — so much so that they become almost minimalist. Much of her new album features a glimmering, cinematic production, which lights up lyrics that can unreel like little psychological essays or resolve into fairly simple pop reveries.

Themes are accented by strings, tasteful bits of guitar, the sounds of birds chirping, and often are anchored by a sturdy, jazz-inflected bass line or a piano figure evoking a Latin influence. An existential jingle such as “To Be Gone” (“I just wanna be / wanna be gone”) feints toward a kind of bolero one moment, and might easily tip over into trip-hop the next. On the other hand, when Ms. Ternheim covers Fleetwood Mac’s “Little Lies,” she settles for buffering the delicate clarity of her voice with a plucked melody on guitar. The spare quality recaptures something touching in Christine McVie’s lyrics that might have been forgotten.

“I’m trying to find the perfect song that’s good either way,” Ms. Ternheim said. “You can put any kind of clothes on music. That version of ‘To Be Gone’ on the album is my favorite version. I’ve done it on piano, on guitar, on harmonium, with a beat, with a band, with a trio, with a synthesizer, but you get something with an acoustic show that you don’t get with a band.”

That approach is not far from how Ms. Ternheim first began performing. More than a decade ago, she was an exchange student living in a placid suburb of Atlanta called Peachtree City, a place where residents often tooled around on golf carts.

“Yeah, I know. It’s crazy,” she said. “I stayed with a couple that wanted to see if they wanted to have a kid, so they got me. They got divorced two years later, but they were great.”

It was 1995, and Atlanta’s buzzing acoustic scene was ideal for the Swedish teen. She would visit Little Five Points, the city’s “alternative” neighborhood, and play open-mic shows. Around the same time, songwriters such as Chan Marshall (aka Cat Power), Joseph Arthur, and the future members of the pop-country act Sugarland were doing much the same thing.

Thirteen years later, Ms. Ternheim has arrived in New York to seize her own moment. And she’s willing to take her chances. As we spoke, she was contemplating a new word she had learned in English — “comfort” — and sorting out how to fit it into a song. “Being comfortable is so deceiving and dangerous,” she said. “People want to be comfortable. That’s nice. But it’s on the edge of things, when things are about to break, when things happen. That’s when you get a lot of ideas flowing.”