# Return Time Plots

## What are Return Time Plots?

Return time plots are a way of graphically representing the most extreme events in a big sample of data, such as weather data or river flows. These types of plot are a convenient way to look closely at the “tail” of a distribution, which is hard to see in detail when you plot the data in a more familiar way, such as in a histogram, where your attention is drawn to the middle of the distribution.

The “return time” of an event, also known as the “return period” or “recurrence interval”, is the likelihood of an event occurring, defined by a particular variable exceeding a certain threshold in a certain time interval. For example, you would say an extreme flood had occurred if rainfall exceeded 350mm during the winter season.

## What does each dot represent?

Final results from the weather@home 2014: UK Flooding Experiment,
showing nearly 40,000 models results: each dot represents one model

In weather@home experiments, each dot on the plot represents a single model simulation which has been run on a participant’s computer. We run tens of thousands of model simulations, which are identical to each other except for their starting conditions, which are varied slightly. These slight differences result in a different outcome in each model for the risk of certain events.

Our weather@home experiments are designed to answer the question: did climate change have an effect on the likelihood of this extreme weather event occurring? They involve comparing two sets of models – one with climate change and one in a “world that might have been” without climate change, which is why there are two colours of dots on these graphs, representing these two sets of models.

When these model simulations are put together to form large ensembles, we can look at the average risk for that particular event. We plot all the individual models on one graph and you can see the curve that emerges, which represents the range of results from the entire ensemble:

If you look at a plot of just a small number of model simulations, and compare it to a plot with tens of thousands, you can see why it’s so important to run these large ensembles of models if you want to get clear, statistically significant results:

Comparison of results from the weather@home 2014: UK Flooding Experiment
with just a few models (left) and tens of thousands of models (right)

## What does the x-axis along the bottom mean?

The x-axis tells us the chance of an event occurring in a given year, such a seasonal rainfall, exceeding a particular threshold. With extreme weather events, we tend to talk about “1 in 10 year events”, which occur quite frequently. The chance of such an event occurring is 1 in 10, or 10%, in any given year.

The further you go to the right of the plot, the rarer the events get, all the way up to “1 in 1000 year events”, which are very rare, having a 0.1% chance of occurring in a given year.

The phrase “1 in 100 year event” does not mean that an event will occur exactly every 100 years, but that the probability is that it will occur once every 100 years.

The x-axis is logarithmic, which means that each number is 10 times bigger than the last (for example 10, 100, 1000), rather than there being the same distance between each (for example 10, 20, 30). This logarithmic scale lets us show a wide range of values more clearly in a single plot.

## What does the y-axis up the side mean?

The y-axis shows the magnitude of the weather event in the form of a threshold. In this example, looking at high rainfall, the y-axis shows the total rainfall during a particular season that exceeded a threshold.

A low rainfall value, such as a winter with only 100mm or more of rain, would be a normal winter in the UK, which does not lead to widespread flooding.

A rainy season, which exceeded 350mm of rain, would be a “1 in 100 year event” and will have led to extreme flooding.

## Why are some graphs the other way up?

When you are looking at the risk of flooding, you are interested in whether rainfall is more than a certain threshold. It’s very likely to exceed a low threshold but increasingly unlikely to exceed a high threshold. This explains why the curve on return time plots for flood risk increase from left to right – more than 100mm of rain falls almost every year (1/1) but more than 350mm of rain only happens 1/1000 years or less.

For drought risk, on the other hand, you are interested in how low the rainfall is. So, it’s very likely that you will get less than a large amount of rain – less than 800mm of rain will occur almost every year – but it’s very unlikely that you will get less than 100mm of rain – this might occur only once every 100 years (1/100):

How can we use Return Time Plots to understand the influence of climate change?