When a newly-elected Justin Trudeau took to the international stage at the COP 21 climate talks in Paris last November, he cheerfully proclaimed "Canada is back!"

The prime minister made an impassioned speech in support of decisive action on climate change, underscoring the "opportunity to make history" with an agreement to limit global temperature increases to 2 C below pre-industrial levels.

This week, in announcing the approval of the tripling in capacity of Kinder Morgan's Trans Mountain pipeline, Trudeau's take was decidedly different.

"There isn't a country in the world that would find billions of barrels of oil and leave it in the ground, while there is a market for it," he said.

How can Canada be an oil sands producer and climate leader at the same time? And more importantly, how can it meet its commitments on both climate change and oil production?

What is Canada's carbon budget?

Calculating Canada's carbon numbers isn't as simple as it sounds.There are two ways of looking at the problem.

Think of the world's carbon output as something like splitting a shared-plate dinner at a restaurant.

When the food comes, should you eat and drink the same amount you've become accustomed to at home? Or should everyone at the table split the food evenly?

Prime Minister Justin Trudeau and Alberta Premier Rachel Notley, left, shake hands during a meeting on Parliament Hill after the federal cabinet gave the green light to Kinder Morgan's Trans Mountain expansion, and Enbridge's Line 3. (Justin Tang/Canadian Press)

By that metaphor, you could argue that Canada is a carbon glutton, trying to stiff the world's more populous nations with an unfair portion of the emissions reduction bill.

We currently emit about two per cent of the world's greenhouse gases, so we would like to claim that portion of the carbon budget as our own.

But UBC professor of climatology Simon Donner says a more realistic way of dividing up the carbon pie might be by population. If you follow that model, all of a sudden Canada has around half a per cent of the world's emissions budget.

"The rest of the world is not going to agree with that two per cent budget," said Donner.

"Canada's going to have to restrict its emissions even more and that makes going ahead with the Trans Mountain expansion look crazy. We're definitely going to blow the budget."

Emissions not going down

More pipeline capacity doesn't necessarily mean more production, but Donner says it's safe to assume output will at least stay consistent at levels that see the oil sands account for 11 to 13 per cent of Canada's carbon numbers.

The B.C. government is planning a boom in LNG production and Trudeau also announced an upgrade to Enbridge's Line 3 project at the same time he approved Trans Mountain.

"The challenge with that, is that it means the rest of the economy takes the burden of reducing emissions," says Donner.

Which means the rest of the economy — industry, agriculture, vehicles, buildings and electricity included — would have to reduce emissions by 35 to 38 per cent.

While that might already make meeting our Paris commitments sound daunting, remember that model uses the two per cent of the world emissions budget. Meeting the budget using a population-based model would be even more difficult.

Carbon tax could be the answer

But other experts say trimming carbon production on a sector-by-sector basis is neither instructive, nor helpful, in trying to square Canada's climate change commitments with its pipeline promises.

Jennifer Winter, the scientific director of energy and environmental policy at the school of public policy at the University of Calgary says the only way to regulate carbon emissions is with a carbon tax.

And by that method — the only way to figure out how to get to the Paris numbers is to calculate what level of tax would be needed to stop industry from polluting beyond the Paris levels.

"If companies find it profitable to build and operate, even in the presence of the carbon tax, then we should allow these projects to go forward," Winter says.

B.C. currently has the highest carbon tax in the country at $30 a tonne. The federal price isn't set to reach $50 until 2022. But University of Calgary economist Trevor Tombe says something in the ballpark of $130 a tonne would be needed to help Canada reach the necessary numbers.

Difficult to meet Paris commitments

With the approval of the Trans Mountain pipeline and other large oil and gas projects and a carbon tax regime still in its infancy, it appears it will be difficult for Canada to meet its Paris emissions targets.

And without an unforseen government intervention to put us back on course, Canada's Paris climate commitments could go up in smoke.