The sunshine boys: Brooklyn's Nada Surf have bounced back with an album of upbeat pop

Happy talk: (far left, from left) Ira Elliott, Daniel Lorca and Caws

Their latest album might be called Lucky but Nada Surf's 15-year career has been anything but. Even their name causes misconceptions: it's so redolent of Californian sunshine that at least one rock encyclopaedia has listed them as natives of Los Angeles – yet they hail from Brooklyn.

And, while every band aspires to instant success, their first single, "Popular", in 1996 proved again that names can be misleading. The novelty hit failed to nudge their debut album High/Low into the US Top 50, while critics cruelly dubbed them "Weezer-lite".

"In our minds we were aiming somewhere between Sonic Youth and Pavement," reveals frontman and songwriter Matthew Caws, conceding: "Nobody else saw that. And I had the same glasses as Rivers Cuomo [Weezer's lead singer]."

Things got worse with the second album The Proximity Effect (1998). Unable to identify a hit single, their label, Elektra, refused to release it in America, and then dropped the band. There was a silver lining when the album came out in Europe, where Nada Surf built a cultish following. But, by the time they finally released it independently in America – following a three-year battle to buy it back from Elektra – Caws was making ends meet by working in his local record store.

Happily, after a four-year hiatus, Nada Surf bounced back with a new independent label and an entirely new sound. In place of the quirky pop-punk that first defined them, they returned with a jangly, harmony-drenched power-pop style on Let Go in 2002, setting melancholy lyrics to uplifting melodies, a recipe continued on The Weight is a Gift three years later, recorded after the birth of Caws's son Theodore.

With the release of Lucky, it seems that Nada Surf – Caws on guitar, his schoolfriend Daniel Lorca on bass, and former Fuzztones drummer Ira Elliot – might have finally turned a corner. The album has an undeniably happy undercurrent to match its sunny sound and optimistic title.

The reasons are not hard to find: since turning 40 last August, single-parenthood, new love and a new decade in life have brought fresh inspiration to Caws's songwriting. He admits he's "starting to feel old" but emphasises: "I will never – and pardon the Hallmark card-ism – be as young as I am right now."

None the less, the album's opening song, "See These Bones", is a strangely exuberant rumination upon mortality inspired by a visit to the catacombs beneath a Roman church, where the Capuchin monks store their dead in macabre displays. Another, "Here Goes Something", openly celebrates the singer's joy at being a single father, while "Ice on the Wing" celebrates an entirely different source of joy – his grandfather's heroic status as a decorated RAF fighter pilot in the First World War.

It's not every day you hear a rock band singing about Sopwith Camels and doodlebugs, but it turns out that Caws, whose parents are both distinguished New York academics, not only boasts a hero of two world wars in his exotically named maternal grandfather Harmon Chadbourn Rorison, but also an English father. "My dad grew up in Southall [west London] in a Plymouth Brethren family," he explains. "They're like an English version of the Amish: they don't consort with anyone from the outside and believe that they are following the word of Christ more closely than anyone else. They believe that the outside world is Satan's world so anything modern is banned: when my dad was growing up during the Blitz they had no newspapers or radio in the house."

When he was 20, Peter Caws told his family he had lost the faith and went to America, where he studied philosophy at Yale, married a student of comparative literature, and became a philosophy professor ("probably because he needed to find reason and logic," observes his son wryly) whose published works include volumes on Sartre and structuralism. Mary Ann Caws, meanwhile, is a professor of comparative literature, whose specialist subject is 20th-century avant-garde literature and art, particularly Surrealism.

Caws grew up in a stuffy, academic world, where popular music was neither discussed nor appreciated ("I asked them what it was like when The Beatles arrived in America and they said: 'Is that the Lennon fellow?'"). He is, however, able to boast – uniquely – that he gave his first public performance in front of one of the world's great philosophers.

"I once played 'Stairway to Heaven' to Jacques Derrida," he announces with a proud smile. "I was about 14 and my mom had given him his first job in the States, so he would come over to dinner. With a lot of hot-headed academics in the room, sometimes people wouldn't get along, so my parents would get me to come out and play to defuse the atmosphere. Later, my sister, who was into New Wave, gave him a song by Scritti Politti called 'Jacques Derrida'."

Pop music was completely absent from the Caws household. "They listened to nothing but classical music: it was all baroque, mostly Bach, but it was fun. I recently bought their favourite record, '1052' [the catalogue number of Bach's Keyboard Concerto No 1 in D minor], and I was totally transported."

Caws's own influences came from a backdrop of disco and "classic rock" on the radio, and his first single was the Sugarhill Gang's "Rapper's Delight". "Then, when I was 11, my best friend's older brother played me the Ramones' Rocket to Russia and The Velvet Underground's Loaded and I totally freaked out. Later I saw Echo and the Bunnymen on their Ocean Rain tour and that inspired me to make my own music."

Despite their sunny sound, the songs on Lucky were mostly written in New York – "some of those on rainy days!" – and recorded in Seattle, which is widely (although, apparently, wrongly) believed to be America's wettest city. Perhaps, Caws argues, it is the very absence of sun that has encouraged him to inject so much warmth and joy into his music. "I guess the honest answer is that I'm always looking to be cheered up by music," he says, "so I'm always looking for sunshine – even in sad songs."

Nada Surf play Koko, London NW1 (0844 847 2258) on Thursday; 'Lucky' is out now on City Slang