Ever since the Clean Power Plan was introduced by the Environmental Protection Agency to crack down on carbon pollution from electricity plants, its advocates have disputed the assertion that it would be unduly burdensome and costly for utility companies. Indeed, they often note, its goals are already almost within reach.

But if that's so, the flip side of their argument is that the plan may not be demanding enough for the U.S. to meet its initial pledges under the new Paris treaty.

Now a new peer-reviewed study by researchers at a national lab offers more evidence that like other government policies aimed at reducing planet-warming emissions of greenhouse gases, the reductions sought under the CPP are too little and too late for the U.S. to keep its Paris promise.

"Additional mitigation measures will probably be required," said the study, published on Monday in the journal Nature Climate Change. It warned that "time is short" to fill the U.S. emissions gap of roughly 1.5 billion tons per year of carbon dioxide.

That's the real reason that this week's oral arguments in litigation brought by coal states and fossil fuel companies to overturn the rules are so momentous. The hearing begins Tuesday before the full United States Court of Appeals for the District of Columbia Circuit.

Even if the Clean Power Plan, the linchpin of President Obama's climate policy, sails through the appeals court and is upheld by the Supreme Court next year, its regulations will only pave the way for stricter reductions in the years to come. Those will include new measures to drive coal use down more steeply and broader rules to cut emissions from other industries, such as refineries.

Presenting legal arguments that by now are familiar, the plan's challengers will emphasize that even the relatively loose and highly flexible strictures of the EPA's approach is an illegal over-extension of federal power. Its defenders will emphasize that the Supreme Court has repeatedly decreed that the Clean Air Act gives the agency the power to control carbon dioxide.

Nobody will dispute that coal has been under assault for years, caught in a pincer between markets and regulations.

Last week, the White House's economic council issued a broad review of climate-related trends that showed a steady decline in overall carbon emissions from the energy industry. They all have worked against coal: the recession that hit just as President Obama was elected; an increase in energy efficiency; and competition from natural gas and renewables.

As a result, a significant part of the emissions decline projected if the Clean Power Plan takes full effect—32 percent by 2030, compared to the levels of 2005—has already been achieved. Several states have already met the early goals of the plan or are close to doing so, five years before the initial deadline in 2022.

Even after the Supreme Court unexpectedly put the Clean Power Plan on hold while the lawsuits run their course, coal's death spiral has continued.

"The electricity industry is and has been for years in a rapid transition away from coal, towards cleaner generation. The transition is driven mainly by fundamental market forces," David Doniger of the Natural Resources Defense Council said recently.

"Analysts expect the power sector to be well positioned to meet the Clean Power Plan's objectives in 2022 and beyond," he said. Not only is cheaper, cleaner natural gas supplanting coal, but so are carbon-free renewables, propelled by advances in technology and by newly extended tax subsidies.

If that's the case, why is the litigation so important?

If the regulations fail in the courts, won't market forces take over and continue to clean up the power plants?

Not entirely, the environmentalists reply. The CPP, which aims to cut emissions from electricity 32 percent by 2030, would not only lock in emissions cuts that are already occurring, but would also send a powerful market signal to keep the momentum alive.

The optimistic portrayal is muddier in the context of U.S. pledges under the new Paris treaty.

In an attempt to make the power plant rules more palatable to states and to industry, the EPA last year adjusted the final version to phase the reductions in more slowly, making the early deadlines easier to meet.

At the Paris negotiations, though, the United States decided to emphasize early action. It pledged to reduce its economy-wide carbon dioxide emissions by up to 28 percent in the year 2025, reasoning that this would spur others to act early—and lead to even more ambitious goals down the line. That is crucial because scientists say the pledges of all the nations combined are inadequate.

It's this combination—weaker early action under the Clean Power Plan, and stronger early pledges in Paris—that leads to the conclusions of the new Nature Climate Change study, written by Jeffrey B. Greenblatt of the Lawrence Berkeley National Laboratory and co-author Max Wei.

Their paper echoes many other studies suggesting that the United States is likely to fall short of its Paris pledges unless even more is done following successful implementation of the Clean Power Plan. (Their analysis also considers other policies, like those affecting auto fuel efficiency and so on.)

"Promising strategies exist spanning multiple sectors and technologies," they wrote. "Time is short, so it is vital for the U.S. to develop achievable plans to maintain pressure on other nations to support the Paris Agreement."

"In the electricity sector, an aggressive phase out of coal and natural gas generation, with accompanying increases in renewables, energy efficiency, and possibly nuclear generation could be enacted," they said.

The burden can't fall entirely on the electricity industry. Almost certainly, success of the Clean Power Plan would lead directly to controls on industries such as oil refining, where emissions are not as big, but still significant.

The EPA and its defenders argue mainly that success of the Clean Power Plan in the courts will ensconce its approach as moderate, flexible, efficient—and legal.

What's left unsaid most of the time is that its doctrine has to be expanded if it is to succeed.