One foggy day last month, Mayor Edwin M. Lee of San Francisco stood on the windswept roof of the California Academy of Sciences. He was there to celebrate what he called the city’s “tremendous accomplishment” in reducing greenhouse gas emissions.

Based on a new analysis by his environmental office, San Francisco had cut carbon emissions by 12 percent since 1990, Lee said, a rate his office said was higher than had been reported by any other American city.

“We did it with basically being smarter, we did it being less wasteful, and then we did it by being innovative in our city,” Lee said, amid applause from city environmental staff members and other officials.

But as the city celebrates, burnishing its green image, some energy experts and environmentalists have raised questions about the city’s calculations. Although San Francisco has taken significant steps to shrink its carbon footprint, these critics said, the numbers are misleading, and the end result is not nearly as green as the city claims.

Eric Brooks, sustainability chairman of the San Francisco Green Party, called the city’s calculations “smoke and mirrors.”

In fact, according to an analysis by The Bay Citizen, the real decrease in carbon emissions may be only one-fourth the percentage cited by the city.

The debate over the exact measurements of San Francisco’s carbon emissions reflects the intensifying politics of green energy. In the Bay Area, environmental credibility can be crucial to political advancement, and even the arcane math behind public policy can provoke profound disagreement.

Lee and his environmental advisers say the main driver of San Francisco’s carbon emission reductions was the closing of inefficient fossil-fuel power plants at Hunters Point in 2006 and in the Potrero neighborhood in 2010.

The city also reported minor emissions reductions from some transit systems, waste management, and natural-gas-burning stoves and other household appliances. Small increases were reported from the Muni transit system and road traffic.

“We reduced our emissions because we stopped getting so much of our power from local dirty power plants,” said Melanie Nutter, director of the San Francisco Environment Department, which established the city’s carbon accounting system in 2004.

During the past decade, the city exerted political and legal pressure on power companies and electricity regulators to close the aging plants. Those privately owned facilities pumped electricity into the Northern California electrical grid owned by Pacific Gas & Electric, which sold the energy to its customers.

State electricity officials allowed the plants to be shut after new electrical cables were laid between the city and large PG&E substations in the East Bay and San Mateo County. Last year, the Trans Bay Cable, a 53-mile underwater cable, was switched on, linking San Francisco with Contra Costa County, where more than 10 power plants operate using fossil fuels; another is under construction.

Nutter said that new natural gas plants that PG&E had added in Northern California, as the city facilities closed down, “operate much more cleanly and efficiently than the old ones in San Francisco did.” With the closing of the Hunters Point and Potrero plants, she said, the city began drawing more electricity from a wide grid of cleaner power, because of a diverse mix of fossil fuel, nuclear and renewable energy sold by PG&E that generates fewer carbon emissions.