A mathematical model has shown for the first time how climate change will increase glacial erosion by speeding up movement of the icy giants.

Using New Zealand's Franz Josef Glacier as a model, a team of international scientists confirmed a theoretical model first proposed in the 1970s by demonstrating that the rate of glacial erosion was proportional to the square of the glacier's speed.

This meant that fast moving glaciers, or portions of glaciers, would erode much more rock than slow-moving glaciers - and the pattern would increase erosion as climate change sped up movement.

The findings, just published in the journal Science, applied to faster-moving glaciers in mountainous mid-latitude regions, such as the Fox and Franz Josef glaciers, but not necessarily to polar glaciers that moved more slowly.

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Study co-author and GNS Science geologist Simon Cox said this "non-linear behaviour" explained the wide range of observed glacial erosion rates - and also the profound impact of glaciation on mountainous landscapes during the past few millions years.

"The erosive power of glaciers varies considerably, with some of the most rapid glacial erosion happening in mid-latitude climates," he said.

"This research confirms that fast glaciers are more effective at gouging landscapes than slow-moving ones."

Although the process of glaciation was widespread in the landscape, scientists did not fully understand it, partly because of the great difficulty accessing the ice-bedrock interface underneath glaciers.

In the study of the Franz Josef Glacier, which took place over a five-month period in 2013 and 2014, the scientists used a combination of two techniques to shed light on the glacier's behaviour.

Firstly, they used satellite imagery to measure the speed of the glacier at its surface, which reaches up to 3m-a-day.

At the same time, they analysed the crystalline structure of carbon-bearing particles - mostly graphite - collected from the meltwater river below the glacier.

To do this, they used a method called Raman spectroscopy, which involves measuring the way light is scattered when it interacts with carbonaceous particles.

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They then used the "Raman signature" to track particles back to the bands of Alpine Schist rocks from where each particle was eroded.

This enabled them to quantify erosion rates beneath the glacier.

From the results, they have developed a law for glacial erosion that captures the variability seen globally, in different climate zones.

Their work shows erosion is highly sensitive to small variations in topographic slope and rainfall.

Dr Cox said the power demonstrated by the combination of techniques would enable scientists to better understand glacial erosion and how this will change as glaciers respond to global warming.

Associate Professor Andrew Mackintosh, deputy director of Victoria University's Antarctic Research Centre, said the study demonstrated how New Zealand glaciers - especially those few that flow very fast - are also capable of eroding the underlying landscape at a fast rate.

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"The broader implications of this study are related to how landscapes evolve through time," he said.

"Glacial erosion is difficult to study because we do not have access to the base of glaciers and the processes there cannot be observed directly.

"However, we know that some glaciers cause very large amounts of erosion while others do not.

"This study helps to explain why glacier erosion rates vary in space and time."

The findings also add to a bleak picture for the future of New Zealand's postcard glaciers.
Earlier this year, Victoria University scientist Dr Brian Anderson told the Herald that, by 2100, they would bear little resemblance to how we know them today.

Recent research had already shown how the Franz Josef and Fox Glaciers, which attract tens of thousands of tourists each year, had retreated by three kilometres and at least between three to four square kilometres in area since the 1800s, with most of the loss happening between 1934 and 1983.

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Although there had been small advances at different points, the overall picture was one of melting - and a retreat observed last year was one of the fastest on record.

An analysis of aerial surveys, published on Australian website The Conversation last year, also showed how a third of the permanent snow and ice on the Southern Alps had vanished in less than four decades.

Partly using aerial surveys by the National Institute of Water and Atmospheric Research, study authors Dr Jim Salinger, Professor Emeritus Blair Fitzharris and Dr Trevor Chinn calculated the alps' ice volume had shrunk by 18.4cu km or 34 per cent - and those ice losses have been accelerating rapidly in the past 15 years.