Humans love comfort (such as a cool drink on a hot day, or a warm fire on a wintery day). But exposure to extremes nearly always tests our comfort zones. As a researcher of extremes, I think about them a lot. I hate them – and in this article I tell you why.

1. Extreme events are devastating

Extreme events, especially extreme rainfall, are devastating – they may cause damage to human life. The flood risk of extreme rainfall is one of the most dangerous natural disasters.

For example, in 2010/11 Queensland suffered a series of floods which caused a reduction of about A$30 billion to Australia’s GDP, and lead to 38 deaths.

2. Extreme events are rare

Extreme events are rare, which means that humans have limited chances to see and observe them. This leads to a lack of data about extreme events, which then makes analysing them difficult.

Our instrumental record has developed since the 1900s, but many features we design for – such as dams – require consideration of significantly rarer floods.

How can we allow for droughts over this period when we may have only seen three events? How can we truly resolve issues of climate variability?

3. Extreme events can be spatially dependent

The spatial dependence of extreme events means that extreme events are related in space. Let’s take extreme rainfall as an example. The figure below shows that extreme rainfall has a clear spatial pattern; the yellow colour shows higher intensity.

Spatial dependence makes estimating floods along linear infrastructures difficult when they are caused by extreme rainfall.

For example, any particular extreme event has an impact on multiple locations along the route. When extreme rainfall occurs and causes flood at one location, it is also likely to occur at another location along the route because there is the spatial dependence between extreme events.

This image depicts rainfall in south eastern Queensland and northern New South Wales. It shows the radar focused on Beenleigh, with a distribution of rain to the west. What you can see in this image is heavy rainfall in the mountain range just out of Brisbane, and becoming more dispersed further away from the centre of the rain activity.

Image of a Bureau of Meterology rain radar.

4. Extreme events can be temporally dependent

Temporal dependence of extreme events means that extreme events are related in time.

The figure below shows a case of temporal dependence of extreme rainfall. Panel (a) shows no temporal dependence when the 1-hour, 3-hour, and 6-hour extreme events are independent. Panel (b) shows strong temporal dependence when the 6-hour event contains the 3-hour event, and the 3-hour event contains the 1-hour event. Panel (c) shows some temporal dependence when the 6-hour event contains the 1-hour event, when the 3 hour event is outside.

Temporal dependence makes it difficult to estimate flood, because the current period rainfall will affect catchment water stores. Those water stores may have an impact on a future flood.

temporal dependence

5. Dependence in extremes is not like dependence in non-extremes

The dependence between variables for non-extremes decreases as the variables become increasingly extreme, but where the dependence between variables for extremes remains high.

The evidence for this is shown on the figure below. In the top row, the dependence of the parent scatter plot is 0.8, but zooming into the extreme events it is only 0.2. It  will drop to zero the more extreme we go.

However, not all cases are like this. The bottom row shows a scatter of two events (e.g. extreme rainfall and extreme tide), which keeps the same correlation in extremes.


(Source: Figure 6.5.20. in Westra et al. 2015)

6. Extreme events can be compound events

Extreme impact is more often caused by the combination of variables or events as a compound event.

For example, heavy rainfall together with high tide will make coastal floods more extreme. Another example is that extreme fires can emerge in times of strong wind and high temperatures.

This means that if you want to understand extreme events, you cannot just look to one driver. You need to look at all the combinations of different variables of extremes. This is not a lovely job because the joint probability of multiple variables is super difficult to analyse.

7. Extreme events can be difficult to model

Modelling extreme events can be hard. I am doing my PhD on the spatial and temporal dependence of extreme rainfall events, which forces me to understand huge amounts of statistical equations and models developed by top statisticians.

For a non-statistician like me, this is really difficult and stressful. There are even some periods of time where I cannot make any progress in understanding these things. The figure below is an example of an ugly and difficult equation which made me sleepless for a long time!


(Source: Padoan et al. 2010, p.22)

8. Extreme events can be hard to observe

Extreme events are devastating and dangerous for people who observe them. Let’s focus on the case of river height as an example.

When extreme rainfall occurs it causes fast-flowing rivers (as in the figure below). These rivers flow with great speed, and can carry many things such as stones, mud, and boughs. It means  you cannot get close to the measuring stick without getting swept away.

fast flowing water

Image source

9. Extreme events are too easily forgotten

Sometimes people are surprised when extreme events happens. But they forget that such an extreme event occurred at their location a long time ago.

Let me take an example from my home country,  Vietnam. In 2008, heavy rainfall occurred and lasted for several days in Hanoi. It caused the biggest flood in recent years, with many lives lost and damage of 3,000 billion VND. In that situation, the total rainfall was from 350 mm – 500 mm. In some areas the total rainfall was even higher – up to 914 mm. It exceeded all forecasts and made people very surprised. But in the past, particularly in the year 1971, there was a big flood caused by heavy rainfall in Hanoi, which was evaluated as the biggest flood in the 20th century in the North of Vietnam.

10. I am doing my PhD about extreme events

Currently it is a difficult time in my life, because I am doing my PhD about extreme events. It requires huge knowledge about statistical of extreme events, containing big, ugly mathematical equations. Some theories about spatial extremes took me several months to understand. It is also very time-consuming to run the model: It takes about 16 hours for each test, and the results are likely to be bad or to generate other issues.

Not many people love extreme events

You can see why I hate extreme events! And I am not the only one. But they still happen, and they have bad impacts on human life. It calls for more research to improve the analyses of extremes. This will then also remind people that extreme events are likely to happen more than they expect – which requires decision-makers to keep an eye on extremes when making decisions.


Padoan, S. A., Ribatet, M. and Sisson, S. A. (2010) ‘Likelihood-Based Inference for Max-Stable Processes’, Journal of the American Statistical Association, 105(489), 263-277.

Westra, S.,Leonard, M., Zheng F. (2015) Interaction of Coastal and Riverine Flooding, Chapter 5, Book 6, in Ball J (Eds) Australian Rainfall and Runoff, Engineers Australia.