VARDO, Norway — The population of the Arctic island of Vardo has shrunk to half of what it was 20 years ago, and the fishing industry that sustained its residents for generations has mostly collapsed.

But the local power company, citing a mysterious surge in electricity demand, began work last month to increase energy supplies, laying a thick new cable in a tunnel under the icy waters that separate the island from the Norwegian mainland.

The new electricity cable, along with the recent appearance of earth-moving equipment atop a rocky plateau overlooking Russia across the sea, points to one business that is flourishing in this part of the Arctic: snooping on Russia’s expanding fleet of nuclear submarines armed with ballistic missiles in the Barents Sea.

The extra electricity is needed to power an American-funded radar system under construction on an island in sight of the Kola Peninsula, a frigid Russian territory studded with high-security naval bases and restricted military zones.