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Multiple potential tipping points in the Earth system that involve alternative states have been identified that are susceptible to anthropogenic forcing. Past events—from millions of years ago to within the last century—have manifest as abrupt changes in climatic indicators such as the temperature record. Recent unprecedented heat waves in Australia, their associated devastation, and the considerations above provide motivation to ask whether the Australian daily maximum temperature record has been subject to such abrupt changes. Using a new diagnostic tool—the Lyapunov plot—here it is shown that multiple temperature transitions have occurred with respect to the maximum daily temperature record in widely separated locations in Australia over the last 150 years. All maximum Lyapunov exponents are positive in sign, indicating that the transitions are chaos-to-chaos transitions, and that the different climate modes identified are likely to be manifestations of distinct chaotic attractors. Many of these events occur simultaneously with transitions or extremes in the major natural cycles affecting Australia’s climate, but this observation is not universal. It is known that chaos-to-chaos transitions can result in changes in the value(s) of the state variable(s) that can range from subtle to severe. Although the identified transitions are not catastrophic, this observation does not rule out the possibility of severe, unprecedented, and discontinuous increases in average daily maximum temperatures occurring in Australia at any time within the next few decades.

Lyapunov Exponents and Temperature Transitions in a Warming Australia