If greenhouse gas emissions continue to increase at current rates, this warming will lead to the widespread thawing of permafrost and the release of hundreds of billions of tonnes of CO2 and billions of tonnes of CH4 into the atmosphere.
There's an estimated 10 million dead mammoths buried in the Arctic permafrost.
But they are mere pussy cats compared to the real danger - 1,700 Gt (billion tonnes) of carbon - representing over 50 years worth of current greenhouse gas (GHG) emissions.
And according to a new study in Nature Climate Change, if we let it all melt it will cost us dear. The researchers calculate that the economic damage that would flow from loss of permafrost and the increased GHG emissions would add up to US$43 trillion.
And the damage doesn't stop there - this would be in addition to at least $300 trillion of economic damage linked to other consequences of climate change.
The attempt to put a cumulative economic value on natural changes in climate that have yet to happen is part of the bid to inform governments of the real costs of climate change - and maybe even persuade them to take it seriously.
And no part of the planet is warming faster than the Arctic, arousing the curiosity of the study's authors, economist Chris Hope of the University of Cambridge and the polar expert Kevin Schaefer of the University of Colorado, as to the environmental and economic impacts of the melting permafrost.
1.7 trillion tonnes of carbon locked up in Arctic permafrost
The two scientists report in Nature Climate Change that if emissions of greenhouse gases continue to rise as they are doing now, the thaw of the permafrost and the loss of the ice caps could release the 1,700 Gt of carbon now locked in as frozen organic matter.
It's there because the Arctic has been much warmer than it is now for long periods of time, with rich vegetation and even temperate rainforests. The result is that its now frozen soils contain huge quantities of organic material that never had a chance to decompose.
Now its release in the form of the GHGs CO2 and methane (CH4) would increase the chances of catastrophic floods, wind storms, heat waves and drought, the accelerated melting of the Greenland (and West Antarctic) ice sheets, rising sea levels, the loss of agricultural land and rising energy demand as more and more people began to depend on air conditioning.
So the total cost of permafrost thaw would be $43 tn. The predicted total cost of climate change by 2200 could reach $369 tn, an increase of 13% on all calculations so far.
Governments - and industry - have tended to resist steps such as a switch to renewable resources and greater care for the remaining forests, on the grounds that change on such a scale imposes economic costs. So estimates of the economic costs of climate change are part of an attempt to persuade nations that to do nothing would be far more expensive.
Researchers have tried to derive the true social costs of, for instance, fossil fuels and the economic setbacks associated with specific climate events such as heat waves in single countries, or even the possible costs in lives and income of multiple impacts across a continent.
Cost of action: $6tn. Net saving: $37 tn
The two scientists used a computer model to simulate the impacts of what is now known as the 'business as usual' scenario, in which the world goes on burning more and more fossil fuels, until the concentrations in the atmosphere of carbon dioxide reach 700 parts per million. Right now, the concentration has just tipped 400 ppm. For most of human history, it has hovered around 270ppm.
"The Arctic is warming roughly twice as fast as the global average", they conclude. "If greenhouse gas emissions continue to increase at current rates, this warming will lead to the widespread thawing of permafrost and the release of hundreds of billions of tonnes of CO2 and billions of tonnes of CH4 into the atmosphere ...
"The extra impacts of the permafrost CO2 and CH4 are sufficiently high to justify urgent action to minimize the scale of the release."
An aggressive strategy to limit thaw in the permafrost, they estimate, could cost $6 tn. That's a huge amount of money - but represents a $37 tn saving against the $43 tn cost of letting it happen.
"We want to use these models to help us make better decisions - linking scientific and economic models together is a way to help us do that", said Dr Hope.
"We need to estimate how much it will cost if we do nothing, how much it will cost if we do something, and how much we need to spend to cut back greenhouse gases."
The paper: 'Economic impacts of carbon dioxide and methane released from thawing permafrost' by Chris Hope & Kevin Schaefer is published in Nature Climate Change.
Tim Radford writes for Climate News Network. Oliver Tickell edits The Ecologist.