Republican presidential nominee Donald Trump has claimed that cutting climate funding would save the U.S. $100 billion over eight years, in another remark that observers say demonstrates the dangers of a potential Trump presidency.

"We're going to put America first. That includes canceling billions in climate change spending for the United Nations, a number [Democratic nominee Hillary Clinton] wants to increase, and instead use that money to provide for American infrastructure including clean water, clean air, and safety," Trump said at an Oct. 31 rally in Warren, Michigan. "We're giving away billions and billions and billions of dollars."

The Republican nominee has stood by these projections even as economists put the global costs of business-as-usual emissions in the trillions of dollars.

In another policy statement released by his team later that day, Trump said he would cancel all "wasteful" climate change spending currently under way by the Obama administration and planned by the Clinton campaign—a sum he said would amount to $100 billion over eight years.

Trump's campaign did not give a specific tally of that figure in an email to Bloomberg, but said it came from "an estimate of what the Obama administration had spent on climate-related programs, the amount of U.S. contributions to an international climate fund that Trump would cancel, and a calculation of what Trump believes would be savings to the economy if Obama's and Clinton's climate policies were reversed."

As Bloomberg noted on Tuesday, however, the estimate largely paraphrases the findings of a 2013 Congressional Research Service report which looked at federal climate change funding from fiscal year (FY) 2008 to budget requests for 2014. It did not look at the administration's spending over eight years. Reporters Dean Scott and Renee Schoof wrote:

The report said that the breakdown in the administration's FY 2014 request of $11.6 billion for these programs was about 68 percent for energy technology, 23 percent for science, 8 percent for international assistance and 1 percent for adaptation to climate change. Trump has said he would also cancel commitments for an international fund to help poor nations reduce carbon pollution and adapt to climate impacts. [....] Roughly one-third of that amount is projected to come from private sources. The U.S. is providing a fraction of the $100 billion total today, with the U.K., the European Union, and more than 30 other nations pledging significant sums.

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Moreover, the Congressional Research Service and Trump appear to be diametrically opposed in their stances on climate change, with the nonpartisan organization having previously written that it is not up for debate, while the GOP nominee has alternately called it a hoax, a myth, and bullshit.

Trump has also regularly called for rolling back regulations on the energy industry, which he has said would reinvigorate the coal industry and generate revenue to spend on "infrastructure," although he tends not to specify what that means. But, as CNBC's Tim DiChristopher recently explained, the windfalls he has promised do not account for the real reasons coal is failing, and rely on non-academic research published by an industry group with ties to Charles and David Koch.

The research "does not actually attribute the gains to a lifting of restrictions, as Trump indicated, but to opening all federal lands to oil, gas, and coal leasing," DiChristopher said.

Trump has also promised to increase hydraulic fracturing, or fracking. He claims his energy policies would increase annual economic output by $700 trillion over the next 30 years and $6 trillion in tax revenues, among other high figures.

But as Harvard's environmental economics program director Robert N. Stavins told the New York Times recently, "Trump's promised support of greater natural gas fracking would actually have the effect of lowering demand for coal, causing more mines to close. He can't have it both ways—talk up expanding natural gas supply when in North Dakota, and talk about bringing back coal mining jobs when in Kentucky!"

"[E]nergy economists dismissed the idea that new drilling could bring enough money to substantially fund such proposals," the Times' Coral Davenport writes. "In 2015, coal, oil, and gas companies paid the federal government $9.6 billion in fees and royalties for drilling on public lands and waters, in a budget of $3.8 trillion. Even with a large expansion of such drilling on public land, experts say it is difficult to predict a new such revenue stream at the scale envisioned by Mr. Trump."

The challenge to Trump's energy claims, Davenport says, is simple: economic reality.