What probability tells us about extreme weather events and climate change
Earl Bardsley is a research associate in the School of Science at the University of Waikato and originator of the idea of pumped storage at Lake Onslow . OPINION: More than 100 years ago, the American astronomer Percival Lowell started making telescope observations of Mars, convincing himself that he saw evidence of a canal-building civilisation there. Climate change is not a myth like Lowells canals. We know that a warmer atmosphere can hold more water vapour and so increase the potential for more intense rainfalls. However, there is risk that like Lowell, we over-interpret what we see as confirmation of what we already believe. READ MORE: * Flood-ravaged Gisborne hit by all the ingredients for the perfect storm * Climate change made the May flooding in Canterbury more severe - researchers * Canterbury floods: Is climate change to blame for severe weather events? Extreme rain events in Auckland and elsewhere can therefore give rise to concerns, perhaps even despair, with respect to accelerating climate change from human activity. Extreme rain events are both rare and variable in size. Using models to attribute a climate change component into a single event will inevitably have a high level of uncertainty . An alternative approach is to deliberately avoid the climate change aspect and simply define the probability of an extreme rain event as being constant from one year to the next. On that basis we can consider how things might pan out for heavy rains. It turns out that the no-climate change model has features that are little different from what might be expected with climate change. As a starting point, the no-change model anticipates that the largest event in the record will get larger as time goes on. Toss a coin for long enough and you will get a run of heads longer than your longest previous run. There is always a larger rain coming sooner or later, with or without climate change. But could the waiting time to the next event be less because of climate change? In the absence of climate change, the likelihood of different waiting times can be easily shown by a probability graph. For example, the bell-shaped dashed curve in the graph above represents how long you might think you have before the next 100-year rain, having just experienced one. The most probable waiting time is the highest point on the curve, sitting at 100 years. However, you wouldnt be surprised if the actual time was a bit more or a bit less than 100 years by this model. In fact, the intuitive bell-shaped probability curve is completely wrong. The true likelihood of possible waiting times to the next 100-year event is given by the exponential fall-away solid curve. This means that in the absence of climate change, the most probable time until the next 100-year rain is actually... zero years! A waiting time of zero is an abstraction, but the important message is that short waiting times are more likely than long waiting times, because the exponential curve is highest on its left-hand side. In fact, there is a 63% chance of getting a 100-year rain event before 100 years is up. Likewise, there is a 63% chance of getting a 50-year event before 50 years, and so on. Experiencing a number of 100-year rain events is therefore not necessarily a climate change concern. There is also the multiplier effect of having many potential event locations that could generate headlines of human impact. The heavy rain event on Waihi Beach on May 29 was of short duration and localised. If you take into account all the days in a year, and the number of New Zealand settlements and cities of Waihi Beach size or greater, its not surprising that a few extreme events will get reported in any one year. The other thing to notice about the exponential curve is its extension to the right, meaning that sometimes there can be a long waiting time before an event. It might happen that 150 years pass before a 100-year rain, followed by another just 6 years later and then another only 1 year after that. This unintuitive pattern could be easily misinterpreted as marking the onset of climate change, despite the event probabilities remaining unchanged. What about an unprecedented rainfall much bigger than anything before? Could that confirm a climate change effect? Given the impact of significant natural events of various kinds through history, it might be thought that the analysis of extremes would have been worked out long ago. However, the theory was only finally completed at the time of World War II by a little-known Russian mathematician, Boris Gnedenko . The Gnedenko model applicable to extreme rains happens to have a long right-hand extension as seen in the graph above. This means that a long enough passage of time with no climate change will eventually yield a massive rainfall event much larger than the most probable magnitude. The Auckland anniversary rainfall event is therefore not necessarily a signal of climate change. It could be just that the Auckland record length is now long enough to get a mega-rainfall. All of this is only to point out that similar time patterns of extreme rainfall events and magnitudes can occur during a defined period with no climate change as during global warming. So we need not be too fearful when unprecedented events come along. This is not to attempt an argument against a global warming contribution in extreme rainfall events. Its just that there is a problem in that the large random noise component in the extremes makes it hard to extract the global warming signal. We should of course keep our emissions obligation to the Paris Agreement, while also strengthening our infrastructure against natural extremes of all types, including droughts as well as floods.