Reaching a tipping point is a bit like knocking over a glass of water: once the water is spilt there is no way of getting it back into the glass. Examples include the melting of the Greenland and West Antarctic Ice sheets – pass a certain temperature and the entire ice sheet will melt – and changes to ocean circulation – warm the Earth enough and ocean circulation will change irreversibly.

The million dollar question is, of course, where do these critical boundaries lie? Many scientists are working hard to try and define them, but one group of researchers now argues that viewing tipping points as single boundaries is too simplistic.

"The idea of global 'tipping points' may be misleading because the word 'points' implies that there is a small number of discrete points that divide the `safe operating space' from the `unsafe space'," explained Marty Anderies from Arizona State University, US. "The problem is that when we move along a dimension on which one of these points lies, the locations of the other `tipping points' change. Thus there are infinitely many tipping points that constitute a planetary boundary."

Take the Amazon rainforest for example. Evidence suggests that the combined pressures of climate change and land-use change are liable to cause an abrupt shift to a savannah state – a regional tipping point. If this does happen, there will be a multitude of knock-on effects with global implications, including shifting vapour flows, which affect temperature and rainfall patterns in other regions, and carbon release, leading to increased global temperatures. Ultimately it is the complex interaction of these local and regional planetary boundaries that might drive us to a global tipping point.

In order to explore the shape of these planetary boundaries, Anderies and his colleagues employed a minimal model of land use and carbon cycle dynamics. Using this model they showed that planetary boundaries interact with each other and shouldn't be considered in isolation. Their findings are published in Environmental Research Letters (ERL).

Anderies likens the concept of planetary boundaries to the coastline of an island surrounded by shark-infested waters. Until now we've tended to think of the boundary as a smooth line, drawn in the sand, but in fact we need to consider an island with a jagged, irregular coastline with many narrow inlets. And it is an island that continually changes shape, with storms causing landslides in one area, while washing up sand onto a beach elsewhere.

In the real world, this translates to a multitude of local and regional planetary boundaries, which can ultimately lead to a global transformation. "Examples include losses of living resources (fish stocks or game populations), invasions of harmful species, degradation of grasslands, replacement of coastal kelp forests by sea urchin barrens, and replacement of coral reefs by algae overgrowth," said Anderies and his colleagues.

Although the scientists didn't create their model to predict how far we are from various planetary boundaries, their model scenarios indicate that we are still a long way from the 'photosynthesis/respiration dynamics of land systems' tipping point – a key component of atmospheric carbon dioxide concentrations and hence global temperatures. However, they caution that their model did not consider methane release or albedo change, both of which could change the shape of this boundary and shrink the safe operating space considerably. For Anderies there is only one important take-home message: "it is probably unwise to underestimate the complexity of planetary boundaries."

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