Research on the South Island's Franz Josef Glacier yielded a formulaic approach to tracking glacial erosion which may help scientists monitor change to respond to global warming.

A group of international scientists, including researchers from New Zealand, have confirmed that the rate of glacial erosion is proportional to the square of the glacier's speed, the New Zealand government's Institute of Geological and Nuclear Sciences said October 9.

In mathematical terms, the formula is E=KV2 where E is the erosion rate of the glacier, K is the strength of the underlying rock, and V is the speed of the glacier whole or part in meters per day.

This means that fast moving glaciers gauge out significantly more rock than slow moving glaciers in a non-linear manner. The formula may apply only to the faster glaciers in mountainous, mid-latitude regions like New Zealand's glaciers but not in Polar regions where glaciers move more slowly.

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It is not a pretty story for a warming Earth, since higher temperatures lead to accelerating glaciers. As glaciers erode, more and more sediment and mud is deposited in alpine streams and rivers as mountains, coasts and landscapes are carved away.

"The erosive power of glaciers varies considerably, with some of the most rapid glacial erosion happening in mid-latitude climates," Co-author on the paper that appeared in Science journal and geologist Simon Cox.

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

Scientists face challenges when researching glaciers due to the difficulty of reaching the interface between ice and bedrock underneath a glacier.

Scientists studying the Franz Josef Glacier over a five year period used satellite imagery to measure its surface speed, and they analysed the crystalline structure of carbon-bearing particles collected from the meltwater river below the glacier. From this they could analyse the erosion rate beneath the glacier and compare it to its speed.

Cox said the research will enable scientists to better understand glacial erosion and how it would change as glaciers responded to global warming. From here, solutions can be implemented.